Checklist for Solving Simultaneous Equations in Secondary 3 Math

Checklist for Solving Simultaneous Equations in Secondary 3 Math

Understanding Simultaneous Equations: The Basics

Let's face it, Secondary 3 math can feel like climbing Mount Everest, especially when you hit simultaneous equations. In today's competitive educational environment, many parents in Singapore are hunting for effective ways to enhance their children's grasp of mathematical concepts, from basic arithmetic to advanced problem-solving. Creating a strong foundation early on can greatly boost confidence and academic performance, helping students handle school exams and real-world applications with ease. For those exploring options like math tuition singapore it's essential to focus on programs that emphasize personalized learning and experienced instruction. This method not only tackles individual weaknesses but also fosters a love for the subject, resulting to long-term success in STEM-related fields and beyond.. Don't worry, lah! This guide is here to help Singaporean parents and students conquer those equations with confidence. Think of it as your trusty Sherpa for the mathematical Himalayas. Looking for singapore secondary 3 math tuition? You're in the right place! We'll cover the fundamentals and help you avoid common pitfalls. We will also touch on related topics such as algebra, problem-solving strategies, and even exam tips.

Checklist for Solving Simultaneous Equations

Here's a handy checklist to guide you through solving simultaneous equations. Think of it as your pre-flight checklist before launching into a problem:

  1. Identify the Variables: What are you trying to find? Assign letters (usually x and y) to represent these unknowns.
  2. Formulate the Equations: Translate the word problem into two (or more) mathematical equations. Each equation represents a relationship between the variables.
  3. Choose a Method: Decide whether to use substitution or elimination. Each has its strengths, so pick the one that seems easiest for the given problem.
  4. Solve for One Variable: Use your chosen method to isolate one variable in terms of the other.
  5. Substitute and Solve: Substitute the value you found back into one of the original equations to solve for the remaining variable.
  6. Check Your Solution: Plug both values back into both original equations to ensure they hold true. In the Lion City's demanding education structure, where educational excellence is crucial, tuition generally applies to private supplementary sessions that offer focused assistance in addition to institutional curricula, aiding learners grasp disciplines and prepare for key tests like PSLE, O-Levels, and A-Levels amid fierce pressure. This private education sector has grown into a multi-billion-dollar market, fueled by families' expenditures in tailored support to overcome skill shortfalls and improve scores, although it frequently increases pressure on young kids. As AI surfaces as a disruptor, delving into cutting-edge Singapore tuition solutions uncovers how AI-enhanced tools are individualizing educational journeys worldwide, delivering responsive tutoring that outperforms conventional methods in effectiveness and involvement while addressing worldwide learning inequalities. In Singapore particularly, AI is revolutionizing the conventional supplementary education approach by allowing affordable , flexible applications that align with national syllabi, potentially cutting fees for households and boosting achievements through data-driven insights, while ethical issues like heavy reliance on digital tools are examined.. This is crucial!
  7. State Your Answer Clearly: Write down the values of both variables, clearly indicating what they represent.

Fun Fact: Did you know that systems of equations have been used for thousands of years? Ancient Babylonians were solving linear equations way back when!

Common Mistakes in Secondary 3 Math

Everyone makes mistakes, but knowing what to watch out for can save you a lot of grief. Here are some common blunders students make when tackling simultaneous equations, especially in the context of secondary 3 math exam preparation:

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  • Misinterpreting the Problem: Not fully understanding the word problem and setting up the equations incorrectly.
  • Sign Errors: Making mistakes with positive and negative signs during substitution or elimination.
  • Arithmetic Errors: Simple calculation mistakes can throw off the entire solution. Double-check your work!
  • Forgetting to Check: Not verifying the solution in both original equations.
  • Not Showing Working: In exams, showing your steps is crucial, even if you get the answer right. You can get partial credit even with a small error!

Subtopic: Exam Strategies for Simultaneous Equations

Here are some exam-specific strategies to help you ace those simultaneous equation questions. Consider this when looking for singapore math tutor.

  • Read Carefully: Take your time to understand the question before attempting to solve it. Highlight key information.
  • Plan Your Approach: Decide which method (substitution or elimination) is most suitable.
  • Show All Working: Even if you can do some steps in your head, write them down. This helps with error checking and earns you marks.
  • Manage Your Time: Don't spend too long on one question. If you're stuck, move on and come back to it later.
  • Double-Check Your Answers: Always verify your solution in the original equations.

Interesting Fact: The elimination method is closely related to matrix operations, a fundamental concept in linear algebra, which you might encounter later in your studies!

Remember, mastering simultaneous equations takes practice. Don't be afraid to ask for help from your teachers, classmates, or even consider secondary 3 math tuition rates singapore if you need extra support. With consistent effort, you'll be solving those equations like a pro in no time! Jiayou!

Method 1: Elimination Method - A Step-by-Step Guide

Checklist for Solving Simultaneous Equations in Secondary 3 Math

Solving simultaneous equations is a crucial skill in Secondary 3 math in Singapore. It's not just about getting the right answer; it's about understanding the process. This checklist will guide you through the Elimination Method, a common technique used in singapore secondary 3 math tuition and beyond. Mastering this method will set a strong foundation for more advanced mathematical concepts. Think of it as leveling up in your math game! This is also relevant for those seeking secondary math tuition.

The Elimination Method: A Detailed Walkthrough

The elimination method involves manipulating the equations to eliminate one variable, making it easier to solve for the other. Here's a step-by-step guide:

  1. Choose the Variable to Eliminate: Look at the coefficients (the numbers in front of the variables) in both equations. Decide which variable (x or y) would be easier to eliminate. Ideally, you want coefficients that are the same number, or easily made the same through multiplication.
  2. Manipulate the Equations: Multiply one or both equations by a constant so that the coefficients of the chosen variable are opposites (e.g., 3x and -3x). This is a crucial step!
  3. Add the Equations: Add the two equations together. The chosen variable should now be eliminated, leaving you with a single equation with one variable.
  4. Solve for the Remaining Variable: Solve the resulting equation for the remaining variable. This is usually a straightforward algebraic step.
  5. Substitute to Find the Other Variable: Substitute the value you just found back into one of the original equations (or any equation from the process) and solve for the other variable.
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  7. Verify Your Solution: Plug both values (x and y) into BOTH original equations to ensure they satisfy both. This confirms your solution is correct.

Fun Fact: Did you know that systems of equations have been used for thousands of years? Ancient Babylonians solved problems using methods similar to what we use today!

Common Mistakes in Secondary 3 Math

Even with a solid understanding, mistakes can happen. Here are some common pitfalls to watch out for in your secondary 3 math journey, especially when tackling simultaneous equations:

  • Incorrect Arithmetic: A simple arithmetic error when multiplying equations can throw off the entire solution. Double-check your calculations!
  • Forgetting to Distribute: When multiplying an equation, remember to distribute the constant to every term in the equation.
  • Sign Errors: Pay close attention to positive and negative signs, especially when adding or subtracting equations. A small sign error can lead to a completely wrong answer.
  • Not Verifying the Solution: Always, always, always verify your solution by plugging the values back into the original equations. This is your safety net!

Subtopic: Dealing with Fractions and Decimals

Sometimes, simultaneous equations involve fractions or decimals. Don't panic! Here's how to handle them:

  • Fractions: Multiply the entire equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
  • Decimals: Multiply the entire equation by a power of 10 (10, 100, 1000, etc.) to eliminate the decimals. Choose the power of 10 that shifts the decimal point enough to make all numbers integers.

Interesting Fact: The elimination method is a powerful tool, but it's not the only one! The substitution method is another popular approach, and sometimes it might be more efficient depending on the problem. Knowing both methods gives you more flexibility, leh!

Additional Tips for Success

  • Practice Regularly: The more you practice, the more comfortable you'll become with the elimination method. Do your homework, and consider doing extra practice problems.
  • Show Your Work: Write down every step clearly. This helps you catch errors and makes it easier for your teacher (or tutor!) to understand your thinking.
  • Seek Help When Needed: Don't be afraid to ask for help from your teacher, classmates, or a tutor if you're struggling. There's no shame in asking for assistance! Singapore secondary 3 math tuition can provide personalized support.
  • Stay Positive: Math can be challenging, but it's also rewarding. Stay positive, believe in yourself, and keep practicing!

By following this checklist and practicing regularly, you'll be well on your way to mastering simultaneous equations and acing your Secondary 3 math exams. Good luck, and remember to have fun with it!

Verifying Solutions in Both Equations

After finding the values of x and y, substitute them back into BOTH original equations to verify they satisfy both conditions. A solution that works in only one equation is not a valid solution to the system. This step confirms accuracy.

Distributing Negatives Carefully

When subtracting equations during elimination, meticulously distribute the negative sign to every term in the subtracted equation. Failure to do so is a common source of errors, especially with multiple terms. Double-check each sign change to avoid mistakes.

Recognizing No Solution/Infinite Solutions

Be alert for cases where elimination leads to a contradiction (e.g., 0 = 5) indicating no solution, or an identity (e.g., 0 = 0) indicating infinite solutions. Understanding these outcomes is crucial for correctly interpreting the system. Don't assume there's always a unique solution.

Method 2: Substitution Method - Mastering the Technique

Isolate Variable

The first crucial step in the substitution method is isolating one variable in one of the equations. In this island nation's demanding education system, where English functions as the main medium of instruction and holds a crucial role in national assessments, parents are eager to support their kids overcome common hurdles like grammar affected by Singlish, vocabulary gaps, and issues in interpretation or essay creation. Establishing robust foundational abilities from primary levels can significantly enhance self-assurance in tackling PSLE components such as contextual authoring and verbal communication, while upper-level learners gain from targeted exercises in book-based review and argumentative papers for O-Levels. For those seeking efficient strategies, delving into English tuition Singapore provides useful insights into programs that sync with the MOE syllabus and highlight interactive learning. This additional assistance not only hones exam techniques through simulated trials and input but also supports home habits like daily book and discussions to nurture long-term linguistic expertise and educational excellence.. This means rewriting one equation so that either 'x' or 'y' is alone on one side of the equals sign. Choose the equation and variable that looks easiest to isolate; sometimes one equation will have a variable with a coefficient of 1, making it a prime candidate. For example, if you have the equations x + 2y = 5 and 3x - y = 1, isolating 'y' in the second equation might be simpler than isolating 'x' in the first. Once isolated, this expression will be substituted into the other equation.

Substitute Correctly

Substitution involves replacing the isolated variable in the *other* equation with the expression you found. This is where careful attention to detail is paramount. Imagine you isolated 'x' and found x = 3y + 2. Now, if the other equation is 2x + y = 7, you must replace 'x' with the entire expression (3y + 2), resulting in 2(3y + 2) + y = 7. Make sure to use parentheses to avoid errors, especially when the expression being substituted has multiple terms or a negative sign. This ensures the entire expression is correctly multiplied or distributed.

Solve Equation

After substituting, you'll have a single equation with only one variable. This equation can now be solved using standard algebraic techniques. In a digital age where ongoing skill-building is vital for career progress and individual improvement, prestigious schools internationally are breaking down obstacles by offering a abundance of free online courses that cover varied subjects from computer science and management to humanities and wellness sciences. These efforts allow students of all backgrounds to utilize top-notch lessons, projects, and resources without the economic burden of standard registration, often through services that offer convenient pacing and interactive elements. Uncovering universities free online courses unlocks pathways to elite institutions' knowledge, allowing driven people to improve at no expense and obtain credentials that improve resumes. By making high-level instruction freely available online, such offerings foster worldwide equity, empower underserved groups, and nurture innovation, demonstrating that excellent information is progressively merely a click away for anybody with online availability.. Expand any parentheses, combine like terms, and then isolate the remaining variable. For example, if you have 6y + 4 + y = 7, combine the 'y' terms to get 7y + 4 = 7. Then, subtract 4 from both sides to get 7y = 3, and finally divide by 7 to find y = 3/7. This step is crucial to finding the numerical value of one of your variables.

Back Substitution

Once you've solved for one variable, you need to find the value of the other. This is done by 'back-substituting' the value you just found into *either* of the original equations, or the isolated equation. Choose the equation that looks easiest to work with. Let's say you found y = 2 and you have x = 3y + 1. Substitute y = 2 into this equation to get x = 3(2) + 1, which simplifies to x = 7. This gives you the complete solution to the system of equations.

Check Solution

The final, and often overlooked, step is to check your solution. Substitute both the 'x' and 'y' values you found back into *both* of the original equations. If both equations are true with these values, then your solution is correct. This is the best way to catch any algebraic errors made along the way. For instance, if your original equations were x + y = 9 and x - y = 5, and you found x = 7 and y = 2, plugging these in confirms 7 + 2 = 9 and 7 - 2 = 5, verifying the solution. Don't be kaypoh and skip this step, okay?

When to Use Which Method: Elimination vs. Substitution

Checklist for Solving Simultaneous Equations in Secondary 3 Math

Solving simultaneous equations can feel like navigating a maze, right? But don't worry, it's totally conquerable! This checklist will help you tackle those problems like a pro, especially useful for your Singapore secondary 3 math tuition journey.

1. Understand the Goal

  • What are we trying to find? Remember, the aim is to find the values of the unknown variables (usually x and y) that satisfy both equations.

2. Inspect the Equations

  • Look for Easy Isolations: Is one of the equations already solved for a variable? (e.g., y = 3x + 2). If so, substitution might be your best friend!
  • Matching Coefficients: Do the x or y terms have the same coefficient (number in front)? If so, elimination is looking promising.
  • Can you easily make coefficients match? Sometimes multiplying one (or both) equations by a number can create matching coefficients.

3. Choose Your Weapon (Method)

  • Substitution:
    • Best when one variable is already isolated or easily isolated.
    • Substitute the expression for that variable into the other equation.
    • Solve the resulting single-variable equation.
    • Substitute the value back into either original equation to find the other variable.
  • Elimination:

    • Best when coefficients of one variable are the same or easily made the same.
    • Add or subtract the equations to eliminate one variable.
    • Solve the resulting single-variable equation.
    • Substitute the value back into either original equation to find the other variable.

    Fun Fact: Did you know that systems of equations have been used for centuries? In this bustling city-state's bustling education scene, where pupils deal with intense demands to thrive in numerical studies from elementary to higher tiers, finding a learning center that combines expertise with true enthusiasm can make all the difference in fostering a love for the subject. Passionate teachers who venture outside rote memorization to encourage analytical problem-solving and tackling competencies are scarce, yet they are essential for aiding learners tackle challenges in areas like algebra, calculus, and statistics. For parents looking for similar dedicated support, Secondary 3 math tuition emerge as a symbol of dedication, driven by educators who are strongly engaged in individual learner's journey. This unwavering enthusiasm converts into tailored lesson approaches that modify to personal requirements, leading in improved performance and a lasting appreciation for mathematics that extends into prospective academic and professional endeavors.. Ancient Babylonians were solving problems that involved multiple unknowns!

4. Execute with Precision

  • Substitution: Be extra careful when substituting expressions with multiple terms. Use parentheses to avoid sign errors!
  • Elimination: Ensure you're adding or subtracting the entire equation, not just individual terms.
  • Double-Check: After finding your values for x and y, substitute them back into the original equations. Do they both hold true? If not, time to hunt for that mistake!

5. Common Mistakes in Secondary 3 Math

Even the best students stumble sometimes. Here's what to watch out for:

  • Sign Errors: A classic! Be super careful with negative signs, especially during substitution and elimination.
  • Incorrect Distribution: When multiplying an equation, make sure you multiply every term.
  • Forgetting to Solve for Both Variables: Don't stop after finding x! You need to find y too (or whatever the variables are).
  • Misjudging the Easier Method: Sometimes, what looks easier isn't. Take a moment to really analyze the equations before committing to a method. Don't be kiasu (afraid to lose out) and rush into it!

    Subtopic: Tackling Word Problems (Turning Stories into Equations)

    • Read Carefully: Understand what the problem is asking. What are the unknowns?
    • Define Variables: Let x = something, y = something else. Be clear!
    • Translate: Turn the word problem into two equations. Look for key phrases like "sum," "difference," "twice," etc.
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    • Solve: Use substitution or elimination to find the values of x and y.
    • Answer the Question: Make sure you're actually answering what the problem asked for. Don't just leave it at x = 5.

6. Seeking Help (It's Okay!)

  • Don't be afraid to ask for help! That's what teachers, tutors, and even classmates are for.
  • Consider Singapore secondary 3 math tuition: A good tutor can provide personalized guidance and help you master these concepts.
  • Online Resources: There are tons of helpful videos and practice problems online.

    Interesting Fact: The equal sign (=) wasn't always around! Before the 16th century, mathematicians used words to express equality. Imagine writing that out every time!

Solving simultaneous equations isn't just about getting the right answer; it's about developing problem-solving skills that will help you in all sorts of situations. So, keep practicing, chiong (put in the effort), and you'll be a math whiz in no time! If your child is struggling, consider looking into Singapore secondary 3 math tuition to give them that extra boost and build a strong foundation for future math success.

Setting Up Equations from Word Problems: Translating English to Math

Checklist for Solving Simultaneous Equations in Secondary 3 Math

Solving simultaneous equations can feel like navigating a maze, kanchiong (nervous) already? But don't worry! This checklist will help you tackle those tricky word problems and ace your Secondary 3 math. This is especially useful for students preparing for their 'O' Levels and those seeking singapore secondary 3 math tuition. We'll break down the process into manageable steps.

  1. Understand the Problem:
    • Read the problem carefully – like, really carefully. Don't just skim!
    • Identify what the problem is asking you to find. What are the unknowns?
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    • Highlight the key information and numbers. These are your clues!
  2. Define Your Variables:
    • Assign variables (like 'x' and 'y') to represent the unknowns.
    • Clearly state what each variable represents. For example: "Let x = the number of apples, and y = the price of one orange."
    • Avoid using the same variable for different things. Confirm plus chop, this will cause confusion.
  3. Formulate the Equations:
    • Translate the English sentences into mathematical equations. This is where the magic happens!
    • Look for keywords like "sum," "difference," "product," "twice," etc., to help you translate.
    • Make sure your equations are balanced. Both sides of the equation must be equal.
  4. Solve the Equations:
    • Choose a method to solve the simultaneous equations: substitution or elimination.
    • Substitution Method: Solve one equation for one variable and substitute that expression into the other equation.
    • Elimination Method: Multiply one or both equations by a constant so that the coefficients of one variable are opposites. Then add the equations to eliminate that variable.
    • Show your working clearly! This helps you (and your teacher) track your steps and identify any errors.
  5. Check Your Answer:
    • Substitute your solution back into the original equations to verify that it satisfies both equations.
    • Does your answer make sense in the context of the problem? For example, can you have a negative number of apples?
    • Write your answer with the correct units (e.g., dollars, kilograms, etc.).

Fun Fact: Did you know that systems of linear equations have been studied since the time of the Babylonians? They used them to solve problems related to agriculture and trade!

Common Mistakes in Secondary 3 Math

Even the best students make mistakes! Here are some common pitfalls to watch out for in Secondary 3 math, especially when dealing with simultaneous equations. Avoiding these errors can significantly improve your performance and boost your confidence.

  • Misinterpreting the Problem: Not fully understanding what the question is asking. This leads to setting up the wrong equations.
  • Incorrect Variable Assignment: Using the same variable for different unknowns or not clearly defining what each variable represents.
  • Arithmetic Errors: Making mistakes in basic calculations, such as addition, subtraction, multiplication, and division. Double-check your work!
  • Forgetting to Distribute: When using the distributive property, forgetting to multiply all terms inside the parentheses.
  • Not Checking the Answer: Failing to substitute the solution back into the original equations to verify its correctness.

Subtopics to Help You Further

  • Understanding the Elimination Method in Detail: This method involves manipulating equations to cancel out one variable, making it easier to solve for the other.
  • Mastering the Substitution Method: Learn how to isolate one variable in terms of the other and substitute it into the second equation.
  • Word Problem Deconstruction Techniques: Develop strategies for breaking down complex word problems into manageable parts.

Interesting Fact: The term "algebra" comes from the Arabic word "al-jabr," which means "reunion of broken parts." It was used by the Persian mathematician Al-Khwarizmi in the 9th century!

With practice and a systematic approach, you can conquer simultaneous equations and excel in your Secondary 3 math. Remember, even if you kena arrow (get confused) sometimes, don't give up! Keep practicing, and you'll get there. And if you need extra help, consider exploring singapore secondary 3 math tuition. Jiayou!

Checking Your Solutions: Ensuring Accuracy and Avoiding Errors

Alright, secondary school warriors! You've conquered the simultaneous equations, found your 'x' and 'y,' and are ready to celebrate. But hold up lah! Before you high-five your calculator, let's talk about the crucial step that separates math champions from, well, those who might need a little more help: checking your solutions.

Think of it like this: you've baked a delicious cake (your solution), but you wouldn't serve it without tasting it first, right? Verifying your answers in simultaneous equations is your taste test – ensuring your hard work pays off with full marks!

Why Bother Checking?

  • Accuracy is Key: Math isn't about getting close; it's about getting it right. Checking guarantees your solution satisfies both original equations.
  • Error Detection: Catches sneaky arithmetic mistakes or algebraic slips you might have missed.
  • Confidence Booster: Walking into an exam knowing your answers are verified? Shiok! That's a confidence boost right there!

The Verification Process: Your Step-by-Step Guide

  1. Grab Your Original Equations: Have them handy. These are your benchmarks.
  2. Substitute, Substitute, Substitute!: Replace 'x' and 'y' in each equation with the values you calculated.
  3. Simplify and Evaluate: Carefully perform the arithmetic on both sides of the equation.
  4. Compare and Confirm: Does the left-hand side (LHS) equal the right-hand side (RHS) for both equations? If yes, you're golden!

Fun Fact: Did you know that the concept of solving systems of equations dates back to ancient Babylonian times? They used methods similar to substitution to solve practical problems involving trade and measurement. Talk about math standing the test of time!

Common Mistakes in Secondary 3 Math

Even the best students sometimes stumble. Here's a heads-up on common pitfalls to avoid, especially crucial as you gear up for your O-Levels. Many students seek singapore secondary 3 math tuition to address these challenges.

  • Arithmetic Errors: Simple addition, subtraction, multiplication, or division mistakes can throw everything off. Double-check every calculation!
  • Sign Errors: A negative sign gone astray can lead to a completely wrong answer. Pay close attention to signs when substituting and simplifying.
  • Incorrect Substitution: Ensure you're substituting the 'x' and 'y' values into the correct places in the equations.
  • Forgetting to Check Both Equations: A solution might work for one equation but not the other. You MUST check both!

Subtopic: Strategies to Minimize Errors

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  • Show Your Work: Don't skip steps! Writing out each step makes it easier to spot mistakes.
  • Use a Calculator Wisely: Calculators are great for complex calculations, but don't rely on them for simple arithmetic you can do in your head.
  • Practice Regularly: The more you practice, the less likely you are to make careless errors.
  • Get a Fresh Perspective: If you're stuck, ask a friend, teacher, or tutor to look over your work. Sometimes a fresh pair of eyes can catch something you missed. Consider singapore secondary 3 math tuition for personalized guidance.

Interesting Fact: The equals sign (=) wasn't always the standard symbol. Before the 16th century, mathematicians used words like "is equal to" or even abbreviations. Robert Recorde, a Welsh mathematician, introduced the modern equals sign in 1557, believing that "noe.2. thynges, can be moare equalle" than two parallel lines.

Real-World Application: Why This Matters

Simultaneous equations aren't just abstract math problems. They have real-world applications in fields like:

  • Engineering: Designing structures and systems.
  • Economics: Modeling supply and demand.
  • Computer Science: Developing algorithms.

Mastering this skill now sets you up for success in future studies and careers. Plus, acing your singapore secondary 3 math exams is a pretty good perk too!

So, there you have it! Checking your solutions isn't just a formality; it's your secret weapon for math success. Embrace it, practice it, and watch your grades soar. Now go forth and conquer those simultaneous equations!

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Frequently Asked Questions


The first step is to choose a method: either substitution or elimination, based on which one seems easier for the given equations.
Use substitution if one equation can easily be rearranged to isolate one variable. Use elimination if the coefficients of one variable are the same or easily made the same.
Multiply one or both equations by a constant so that the coefficients of one variable are the same (or opposites).
Substitute the value you found back into either of the original equations and solve for the remaining variable.
Substitute both x and y values into both original equations. If both equations hold true, your solutions are correct.