Checklist for tackling simultaneous equations in O-Level Math

Checklist for tackling simultaneous equations in O-Level Math

Understanding Simultaneous Equations

**

Your Ultimate Checklist for Tackling Simultaneous Equations in O-Level Math

** Sure, we've all been there. Your secondary school kid is struggling with simultaneous equations, and you're wondering how you can help. Well, you're in the right place! Let's dive into this math adventure together, shall we? **

1. Understand the Basics: What are Simultaneous Equations?

** Imagine you're in a magic show. The magician asks you to solve two riddles at the same time. That's what simultaneous equations are like - two or more equations with the same variables that you need to solve together. Fun fact: The concept of simultaneous equations has been around since ancient times, with early examples found in Chinese and Indian mathematics! **

2. Types of Simultaneous Equations: The Math Magician's Tricks

** Just like a magician has different tricks, simultaneous equations come in various forms: - **

Linear Simultaneous Equations

**: These are like two simple riddles. For example, if the magician asks, "I have two apples and three oranges. How many fruits do I have?" and "I have a total of five fruits." You can solve these two equations simultaneously to find the answer. - **

Non-Linear Simultaneous Equations

**: These are trickier, like riddles with variables squared or cubed. For instance, the magician might ask, "The sum of my apples and oranges is five, and the product is ten." Now, you'll need to solve a quadratic equation to find the answer. **

3. Why are Simultaneous Equations Important? The O-Level Math Tuition Angle

** You might be wondering, "Why do I need to learn this?" Well, simultaneous equations are crucial for solving real-life problems, like balancing your budget (yes, math is in your wallet too!) or understanding scientific phenomena. In Singapore, mastering simultaneous equations is essential for acing your O-Level Math exams. That's why many parents opt for O-Level math tuition to help their kids grasp these concepts better. **

4. Common O-Level Math Exam Mistakes: The Math Magician's Trickiest Riddles

** Even the smartest kids can fall into these traps. In the city-state of Singapore's intense academic environment, the Primary 6 year signifies the final phase of primary education, where learners integrate prior education to prepare for the vital PSLE exam, facing escalated subjects like advanced fractions, proofs in geometry, speed and rate problems, and extensive study methods. Guardians often see that the jump in complexity could result in anxiety or gaps in understanding, notably with math, motivating the requirement for expert guidance to hone abilities and test strategies. In this pivotal stage, in which each point matters for secondary placement, extra initiatives prove essential for focused strengthening and confidence-building. online tuition delivers in-depth , PSLE-oriented sessions that align with the current MOE curriculum, incorporating practice tests, error correction workshops, and adaptive teaching methods to address unique student demands. Experienced educators stress effective time allocation and higher-order thinking, assisting pupils tackle the most difficult problems smoothly. In summary, such expert assistance also boosts results ahead of the national assessment and additionally cultivates focus and a love toward maths which continues into secondary education and further.. Here are some common mistakes to watch out for: - **

Not understanding the problem

**: Make sure your kid reads the question carefully before solving. - **

Guessing

**: Encourage your child to work through the problem systematically, not randomly. - **

Making careless mistakes

**: Double-check the answers, as simple errors can cost marks. **

5. Tips for Solving Simultaneous Equations: The Math Magician's Secret Tricks

** In Singapore's challenging post-primary schooling environment, the shift from primary school introduces pupils to more complex mathematical concepts like introductory algebra, integers, and geometric principles, these often prove challenging without adequate preparation. Numerous parents prioritize extra support to fill any gaps and nurture an enthusiasm toward mathematics early on. Singapore Secondary 1 Math Tuition provides targeted , MOE-aligned classes featuring seasoned educators that highlight analytical techniques, personalized guidance, and engaging activities to build basic abilities. The programs often incorporate limited group sizes for improved communication plus ongoing evaluations to track progress. In Singaporean demanding secondary education system, pupils gearing up for the O-Level examinations often face intensified challenges with math, including higher-level concepts such as trigonometry, calculus basics, and plane geometry, that demand strong understanding of ideas and application skills. Families regularly look for specialized support to ensure their teenagers are able to manage curriculum requirements while developing exam confidence through targeted practice plus techniques. math tuition delivers essential reinforcement via Ministry of Education-matched programs, seasoned tutors, and tools such as old question sets and practice assessments to tackle personal shortcomings. The initiatives highlight analytical methods and time management, aiding students achieve better grades on O-Level tests. Ultimately, putting resources in such tuition not only equips pupils ahead of national tests while also establishes a strong base for further education in STEM fields.. Ultimately, putting resources in these foundational programs not only improves academic performance while also arms young learners with upper secondary demands plus sustained achievement within STEM disciplines.. Here are some strategies to help your kid solve simultaneous equations: - **

Substitution

**: Solve one equation for one variable, then substitute that value into the other equation. - **

Elimination

**: Make the coefficients of one variable the same in both equations, then solve for that variable. - **

Graphical

**: Plot both equations on a graph and find the point where they intersect. **

6. What if...? The Future of Math in Singapore

** Imagine if magicians could use math to predict the future. Well, that's what scientists are doing with simultaneous equations, using them to model complex systems and predict outcomes. In Singapore, math is a crucial skill for many industries, from finance to technology. So, helping your kid master simultaneous equations isn't just about acing the O-Levels - it's about setting them up for a bright future! So, there you have it! With this checklist, you're now equipped to help your kid tackle simultaneous equations like a pro.

Choose an Appropriate Method

Decide on the method to solve the simultaneous equations based on the given equations. Methods include substitution, elimination, or matrix method.

Check for Consistency

Ensure that the coefficients of the variables are consistent. If they're not, you might have made a calculation mistake. Also, check if the equations are independent or dependent.

Understand the Problem

Carefully read and comprehend the simultaneous equations given. Identify the number of variables and equations. Check if the equations are linear or non-linear.

Identifying Common O-Level Math Mistakes

Checklist for Tackling Simultaneous Equations in O-Level Math

Ah, simultaneous equations! They're like a math dance, where two equations move in sync, trying to find the same solution. Let's make sure your child isn't stumbling on the dance floor with these common mistakes.

1. In Singapore's structured secondary-level learning pathway, Secondary 2 learners begin handling more intricate mathematical topics including equations with squares, congruent figures, and handling stats, which develop from year one groundwork and prepare for upper secondary demands. Parents commonly search for supplementary resources to enable their teens adjust to such heightened difficulty while sustaining consistent progress under academic stresses. Singapore Secondary 2 Math Tuition offers tailored , Ministry of Education-aligned classes with skilled instructors who apply dynamic aids, real-life examples, plus targeted exercises to enhance comprehension and assessment methods. These sessions foster self-reliant resolution while tackling unique difficulties like algebraic manipulation. In Singaporean secondary-level learning environment, the shift between primary and secondary phases exposes pupils to higher-level abstract maths principles such as algebraic equations, geometric shapes, and data management, which often prove challenging absent adequate support. A lot of parents recognize this key adjustment stage requires extra strengthening to enable adolescents cope with the heightened demands and maintain excellent educational outcomes amid a high-competition setup. Building on the basics laid during PSLE readiness, dedicated courses are vital to tackle personal difficulties and encouraging independent thinking. best math tuition singapore delivers tailored lessons matching Singapore MOE guidelines, integrating interactive tools, demonstrated problems, and problem-solving drills to render education stimulating while efficient. Qualified tutors focus on bridging knowledge gaps from earlier primary stages while introducing approaches tailored to secondary. In the end, this early support also improves grades and assessment competence while also cultivates a more profound interest in math, preparing pupils for O-Level success plus more.. In the end, this focused assistance boosts overall performance, alleviates anxiety, and creates a solid path toward O-Level excellence and future academic pursuits.. Not Understanding the Basics

Before diving into simultaneous equations, ensure your child understands linear equations in slope-intercept form (y = mx + b). This is like learning to walk before running, lah!

2. Mixing Up the Methods

There are two main methods to solve simultaneous equations: substitution and elimination. Each has its own rhythm, like learning a new dance. Make sure your child practices both to find their groove.

  • Substitution: This is like following a recipe. Solve one equation for one variable, then substitute that into the other equation.
  • Elimination: This is like playing a game of Simon Says. Choose a variable, then perform operations on both equations to make that variable's coefficient the same (or zero).

3. Careless Algebra

Be on the lookout for these common slip-ups:

  • Not distributing properly (e.g., 3(x + 2) ≠ 3x + 6)
  • Changing the original equations (make sure to keep them the same throughout the solving process)
  • Making sign errors (be extra careful with plus and minus signs)

4. Checking the Answer

After solving, your child should check their answer by substituting the solution back into the original equations. If both equations equal zero, they've found the right solution. If not, it's back to the drawing board!

Fun Fact: The earliest known record of simultaneous equations was found in a Chinese mathematical work, "Jiuzhang Suanshu," written around 200 BCE. Isn't it amazing how math has been solving mysteries for centuries?

So, parents, keep these common mistakes in mind and help your child practice, practice, practice! With the right O-Level math tuition, they'll be dancing their way to an A* in no time. Now, go forth and conquer those simultaneous equations!

Graphical Approach: A Visual Guide

Understanding Graphs

Before diving into the graphical approach to solve simultaneous equations, it's crucial to understand what graphs represent. In the context of O-Level Math, graphs are visual representations of equations, plotting points that satisfy the equation's conditions. In Singapore's high-speed and academically rigorous setting, guardians acknowledge that establishing a solid learning base as early as possible can make a profound effect in a child's future success. The path toward the PSLE begins much earlier than the testing period, because early habits and skills in disciplines such as math establish the foundation for more complex studies and critical thinking capabilities. By starting preparations in the first few primary levels, pupils can avoid frequent challenges, develop self-assurance gradually, and cultivate a optimistic mindset towards tough topics set to become harder in subsequent years. top math tuition centres in Singapore serves a crucial function in this early strategy, providing child-friendly, captivating lessons that present basic concepts including elementary counting, shapes, and simple patterns aligned with the Ministry of Education syllabus. These programs employ enjoyable, engaging approaches to arouse enthusiasm and avoid knowledge deficiencies from arising, promoting a smoother progression through subsequent grades. Finally, investing in these beginner programs not only alleviates the stress from the PSLE while also equips kids with lifelong thinking tools, providing them a competitive edge in Singapore's achievement-oriented society.. Imagine it like a treasure map, where each point on the map (graph) is a potential treasure (solution) to your equation.

Graphs of Linear Equations

Linear equations, like y = 2x - 3, produce straight line graphs. To graph a linear equation, you'll need to find two points that satisfy the equation and then plot them. Remember, 'y-intercept' is the point where the line crosses the y-axis, which can be found by setting x to 0 in your equation. For instance, in y = 2x - 3, the y-intercept is -3.

Graphs of Quadratic Equations

Quadratic equations, like y = x^2 - 5x + 6, produce parabola-shaped graphs. To graph a quadratic equation, you'll need to find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a. For instance, in y = x^2 - 5x + 6, the x-coordinate of the vertex is -(-5)/2*1 = 2.5. Plotting this point and the y-intercept (found by setting x to 0) will help you draw the parabola.

As the city-state of Singapore's education structure puts a strong emphasis on maths mastery right from the beginning, families are more and more prioritizing organized assistance to help their children navigate the escalating difficulty within the program during initial primary levels. In Primary 2, students face higher-level topics like regrouped addition, introductory fractions, and measurement, which develop from basic abilities and lay the groundwork for advanced problem-solving required for future assessments. Acknowledging the value of ongoing strengthening to avoid beginning challenges and cultivate passion in the discipline, a lot of opt for tailored courses in line with Ministry of Education standards. Singapore Singapore Math Tuition delivers specific , dynamic sessions designed to make those topics accessible and fun via interactive tasks, graphic supports, and personalized input by qualified educators. This approach not only aids kids master current school hurdles while also builds analytical reasoning and resilience. In the long run, this proactive support contributes to more seamless learning journey, minimizing pressure as students prepare for key points such as PSLE and establishing a optimistic path for lifelong learning..

Solving Systems Graphically

To solve a system of simultaneous equations graphically, you'll need to graph both equations on the same coordinate plane. The point where the two graphs intersect is the solution to the system. Remember, the graphs will only intersect at one point if the two equations are linear and non-parallel. If the graphs don't intersect (or intersect at infinity), the system has no solution.

Reading Graphs

Once you've found the intersection point, you can read the solution directly from the graph. The x-coordinate of the intersection point is the solution to the x-variable, and the y-coordinate is the solution to the y-variable. For instance, if the intersection point is (3, 4), then the solution to the system is x = 3 and y = 4.

Step-by-Step: Elimination Method

**Embarking on the Math Adventure: Unravelling Simultaneous Equations** *Alright, mummy and daddy, gather 'round! We're about to dive into the world of secondary school math, where numbers and equations dance together in a beautiful ballet. Today, we're going to tackle simultaneous equations, a topic that might seem daunting, but with the right method, it's like solving a fun puzzle!* **The Elimination Method: Your Secret Weapon** Imagine you're in a bustling hawker centre, and you've got two coupons, each with a different dish number. In Singapore, the schooling framework culminates early schooling years through a nationwide test that assesses students' educational accomplishments and determines their secondary school pathways. This exam gets conducted every year for students during their last year in primary school, highlighting essential topics for assessing comprehensive skills. The PSLE functions as a reference point for placement into appropriate high school streams depending on scores. The exam covers areas like English, Maths, Sciences, and Mother Tongue, having layouts refreshed occasionally to match schooling criteria. Grading is based on Achievement Bands from 1 to 8, such that the aggregate PSLE mark is the sum from each subject's points, influencing long-term educational prospects.. You want to redeem both, but the auntie at the counter can only see one coupon at a time. Sounds like a pickle, right? Well, that's where the elimination method comes in - it's like clearing one coupon from your sight so auntie can see the other. Here's how it works: 1. **Understanding the Basics** - Simultaneous equations are like two equations stuck together, each with two variables (usually x and y). - The goal? To find the values of x and y that satisfy both equations. 2. **The Magic of Elimination** - The elimination method helps you 'eliminate' one variable, leaving you with a simple linear equation. - You can do this by adding, subtracting, multiplying, or dividing the equations to make one variable's coefficient zero. 3. **The Art of Manipulation** - Let's say you've got two equations:

3x + 2y = 13

and

2x - y = 5

. - To eliminate y, you can multiply the second equation by 2, giving you

4x - 2y = 10

. In Singaporean challenging educational framework, the Primary 3 level represents a key change where learners dive more deeply into subjects like multiplication facts, basic fractions, and basic data interpretation, expanding upon prior knowledge to ready for higher-level analytical skills. Many families notice that school tempo alone could fall short for each student, prompting them to look for additional help to foster mathematical curiosity and stop early misconceptions from taking root. During this stage, tailored learning aid becomes invaluable for maintaining educational drive and fostering a positive learning attitude. Singapore O Levels Maths Tuition delivers concentrated, MOE-compliant teaching via compact class groups or individual coaching, highlighting heuristic approaches and visual aids to simplify difficult topics. Educators frequently integrate gamified elements and frequent tests to monitor advancement and increase engagement. Ultimately, this proactive step not only boosts current results while also establishes a solid foundation for excelling at advanced primary stages and the upcoming PSLE.. - Now, add this to the first equation:

(3x + 2y) + (4x - 2y) = 13 + 10

, which simplifies to

7x = 23

. 4. **Solving for x and y** - Divide both sides by 7 to find x:

x = 23 / 7

. - Now, substitute x back into one of the original equations to find y. Using

2x - y = 5

, we get

-y = 5 - (2 * 23 / 7)

, which gives us

y = -19 / 7

. *Fun Fact: The elimination method is like a mathematical game of whack-a-mole, where you 'whack' one variable to find the other!* **Avoiding O-Level Math Exam Pitfalls** Now, you might be wondering, "What if I make a mistake in my manipulation?" Well, that's where understanding common O-Level math exam mistakes comes in handy. - *Careless Errors*: A small slip in calculation can lead to big mistakes. So, always double-check your work! - *Misinterpreting the Question*: Make sure you understand what the question is asking. Read it carefully, and don't make assumptions. - *Inadequate Practice*: The more you practice, the better you get. So, don't shy away from past-year papers and additional practice questions. **When the Going Gets Tough, Seek O-Level Math Tuition** If your child is struggling with simultaneous equations or other math topics, consider O-Level math tuition. These services provide personalized guidance and help students understand complex concepts better. With the right tuition, your child can gain the confidence and skills needed to ace their O-Levels. *Interesting Fact: In Singapore, math tuition is so popular that it's often joked that every student has a 'second home' at their tuition centre!* **The Future is Bright** So, there you have it! With the elimination method under your belt, you're well on your way to tackling simultaneous equations. Remember, every math challenge is like a puzzle waiting to be solved. So, keep practicing, and who knows, you might just become the next math whiz!

Step-by-Step: Substitution Method

**

Let's Get Started: Our Substitution Method Adventure

** Imagine you're in a secret agent's lair, trying to crack a code. Instead of numbers, you're dealing with equations - but the principle's the same! Welcome to our exciting journey through the **Substitution Method** for solving simultaneous equations. So, grab your secret decoder ring, and let's dive in! **

First things first: What are simultaneous equations?

** In simple terms, it's like a riddle with two parts, each trying to trick you. They look something like this: 1. 3x + 2y = 13 2. 5x - 3y = 2 **

Fun Fact!

** Did you know? The study of equations dates back to ancient civilizations like Egypt and Babylon. They used them to solve practical problems, like dividing land or calculating the height of a pyramid! **

So, what's the substitution method?

** The substitution method is like finding a secret password that unlocks both riddles. We'll turn one equation into a simple equation in terms of one variable, then use that to solve for the other variable. Let's see how! In Singapore's performance-based schooling structure, Primary 4 serves as a pivotal turning point where the syllabus escalates featuring subjects like decimal operations, symmetry, and elementary algebraic ideas, testing students to apply logic through organized methods. Numerous parents realize that classroom teachings alone could fail to adequately handle unique student rhythms, leading to the search for extra aids to solidify concepts and sustain sustained interest in math. As preparation toward the PSLE builds momentum, consistent exercises is essential to mastering those core components minus stressing developing brains. tuition services delivers customized , engaging coaching that follows Singapore MOE criteria, incorporating practical illustrations, brain teasers, and digital tools to transform abstract ideas concrete and enjoyable. Qualified instructors prioritize spotting areas for improvement early and turning them into strengths with incremental support. In the long run, this dedication builds resilience, better grades, and a effortless transition to advanced primary levels, setting students on a path to academic excellence.. **

Step 1: Choose your weapon - an equation!

** Pick one of the equations to solve for one variable. Let's solve the first equation for x: 3x + 2y = 13 ⇒ 3x = 13 - 2y ⇒ x = (13 - 2y) / 3 **

Step 2: Substitute and solve!

** Now, substitute this expression for x into the second equation: 5x - 3y = 2 ⇒ 5((13 - 2y) / 3) - 3y = 2 ⇒ (65 - 10y) / 3 - 3y = 2 ⇒ 65 - 10y - 9y = 6 ⇒ -19y = -61 ⇒ y = 61 / 19 **

Interesting Fact!

** The word 'algorithm' comes from the name of a 9th-century Persian mathematician, Muhammad ibn Musa al-Khwarizmi. His book, "The Compendious Book on Calculation by Completion and Balancing," introduced the concept of solving equations algebraically. **

Step 3: Find the other variable

** Now that we have y, we can find x using the expression we found earlier: x = (13 - 2y) / 3 x = (13 - 2(61 / 19)) / 3 x = (13 - 122 / 19) / 3 x = (223 - 122) / 57 x = 101 / 57 **

Common O-Level Math Exam Mistakes: Don't make these!

** 1. **Careless Errors**: Double-check your calculations to avoid silly mistakes. 2. **Not Checking Answers**: Always check if your solution makes sense in the original equations. 3. **Giving Up Too Soon**: Keep trying, and you'll crack it! **

What if... you need more practice?

** Consider **O Levels math tuition** for extra guidance. Many Singaporean parents find this helpful for their secondary 4 kids. It's like having a secret math mentor! **

History of Math Tuition in Singapore

** Math tuition in Singapore started in the 1970s when parents realized the need for extra help. Today, it's a thriving industry, with many centres offering personalized learning. **

So, what's next?

** Now that you've mastered the substitution method, try it on more equations. Practice makes perfect, and soon, you'll be a simultaneous equation-solving ninja!

Practice Problems and Tips

**

Navigating O-Level Math: A Parent's Guide to Simultaneous Equations

** **

Embarking on the O-Level Math Journey

** Imagine your child is a brave explorer, about to embark on a grand adventure through the mysterious jungle of O-Level Math. As a parent, you're their trusted guide, ensuring they have the right tools and knowledge to conquer the challenges ahead. Today, we're gonna tackle one of the trickiest beasts in this jungle - simultaneous equations. **

As Primary 5 introduces a increased layer of intricacy throughout the Singapore maths curriculum, featuring ideas like proportions, percentage concepts, angular measurements, and sophisticated problem statements calling for keener analytical skills, guardians commonly search for approaches to make sure their youngsters keep leading without falling into typical pitfalls in comprehension. This period is critical because it seamlessly links to readying for PSLE, in which cumulative knowledge is tested rigorously, rendering prompt support key in fostering resilience in tackling multi-step questions. As stress mounting, expert support assists in converting possible setbacks to avenues for development and expertise. tuition equips students via tactical resources and personalized coaching matching Singapore MOE guidelines, using techniques including diagrammatic modeling, bar graphs, and practice under time to illuminate intricate topics. Dedicated tutors prioritize conceptual clarity over rote learning, promoting dynamic dialogues and mistake review to impart self-assurance. At year's close, students usually demonstrate notable enhancement in test preparation, paving the way to a smooth shift into Primary 6 plus more within Singapore's intense educational scene..

Understanding the Beast: Simultaneous Equations

** Simultaneous equations are like a pair of mathematical detectives, working together to solve a mystery. They look something like this: 1. Equation 1: 2x + 3y = 13 2. Equation 2: 3x - 2y = 5 To solve this case, your child needs to find the values of x and y that satisfy both equations. It's like finding the perfect balance between two clues to crack the case. **

Calling in the Reinforcements: O-Level Math Tuition

** In Singapore, many parents engage O-Level math tuition centres to give their children an extra boost. These centres provide tailored guidance, helping students understand complex concepts and build confidence. Here are some popular methods used: - **Graphical Method**: Plotting the equations on a graph and finding the intersection point. - **Substitution Method**: Solving one equation for one variable, then substituting that value into the other equation. - **Elimination Method**: Manipulating the equations to make one variable disappear, then solving for the remaining variable. **

Common O-Level Math Exam Mistakes: The Perils of the Jungle

** Even the most experienced explorers can stumble in the jungle. Here are some common mistakes to watch out for: - **Careless Errors**: Double-checking answers can save your child from losing marks due to silly mistakes. - **Not Understanding the Problem**: Encourage your child to read questions carefully and ensure they understand what's being asked. - **Giving Up Too Soon**: Remind them that even the trickiest equations can be solved with patience and the right approach. **

"What if...": A Real-Life Application

** What if your child could use simultaneous equations to solve real-world problems? For instance, they could calculate how long it takes to travel a certain distance if they know the speeds of two different modes of transport. *Fun Fact*: Did you know that the ancient Babylonians were solving simultaneous equations as early as 2000 BCE? They used these methods to divide fields and other practical problems. **

You're Not Alone: Stories from the Jungle

** Remember, every explorer gets stuck sometimes. Even Albert Einstein struggled with math in his early years! But with perseverance and the right guidance, your child can conquer simultaneous equations and many other challenges in the O-Level Math jungle. *Interesting Fact*: The word 'simultaneous' comes from the Latin 'simul', meaning 'at the same time', and 'tāns', meaning 'stretched'. **

Packing Your Backpack for the Journey Ahead

** As we wrap up, here's a checklist to help your child prepare for their O-Level Math adventure: - Understand the basic concepts of simultaneous equations. - Practice, practice, practice! Use past-year papers and online resources. - Learn from mistakes and ask for help when needed. - Remember, every challenge is an opportunity to learn and grow. So, parents, are you ready to guide your child through the O-Level Math jungle? With the right tools, encouragement, and perhaps some O-Level math tuition, your child can emerge victorious. *History Lesson*: The O-Level examinations were first introduced in Singapore in 1951, marking a significant milestone in the country's education system. Since then, they've played a crucial role in shaping the future of countless students.

Check our other pages :

Frequently Asked Questions

Identify the type of simultaneous equations you have. There are three types: linear, quadratic, and exponential.
You can use either the substitution method or the elimination method. The graphing method is also an option, but its less common.
In the substitution method, youll solve one of the equations for one variable, then substitute that expression into the other equation.
Substitute the found values back into both original equations. If both equations are satisfied, your solution is correct.
You can still use the elimination or substitution methods, but youll need to be careful with the order you choose your variables. You can also use matrices for larger systems.