How to Solve Simultaneous Equations Using Elimination Method

PDF download Download Article
PDF download Download Article

Have you ever had a simultaneous problem equation you needed to solve? When you use the elimination method, you can achieve a desired result in a very short time. This article can explain how to perform to achieve the solution for both variables.

Steps

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/0a\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-1.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-1.jpg","bigUrl":"\/images\/thumb\/0\/0a\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-1.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [1]
    • 3x - y = 12
    • 2x + y = 13
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/20\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-2.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-2.jpg","bigUrl":"\/images\/thumb\/2\/20\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-2.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    3x - y = 12 as number one, and 2x + y = 13 as number two. [2]
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/8\/8c\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-3.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-3.jpg","bigUrl":"\/images\/thumb\/8\/8c\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-3.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [3]
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/11\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-4.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-4.jpg","bigUrl":"\/images\/thumb\/1\/11\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-4.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Remember subtraction can also be referred to as the addition of a negative number. If the signs are the same, subtract both equations. If they are different then add the equations. [4]
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/54\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-5.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-5.jpg","bigUrl":"\/images\/thumb\/5\/54\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-5.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Divide both sides by the coefficient of the left side. Take 5 to the other side.It will look like this:x = 25/5. [5]
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b6\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-6.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-6.jpg","bigUrl":"\/images\/thumb\/b\/b6\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-6.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
  7. Use the value of x that was obtained above into either equation (but stick with this equation for the time being). Substitute this value of x into the equation. [6]
  8. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/29\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-8.jpg\/v4-460px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-8.jpg","bigUrl":"\/images\/thumb\/2\/29\/Solve-Simultaneous-Equations-Using-Elimination-Method-Step-8.jpg\/aid3229288-v4-728px-Solve-Simultaneous-Equations-Using-Elimination-Method-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Substitute both the values into the other equation. If the two side numbers at the very end equal each other, you've correctly solved this system of simultaneous equations. [7]
    • 3x - y = 12
    • 3(5) - 3 = 12
    • 15 - 3 = 12
    • 12 = 12
    9. Advertisement

Community Q&A

Search
Add New Question
  • Question
    How do I find the first term and the constant difference of simultaneous equations?
    Donagan
    Top Answerer
    "First term" and "constant difference" do not apply to simultaneous equations. (They are used in arithmetic sequences.)
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 15 Helpful 36
  • Question
    Is this useful in all the countries? Where I live, we work our equations very differently.
    Donagan
    Top Answerer
    Mathematics knows no national boundaries. There is more than one method of solving simultaneous equations, and all methods are known and "useful" in every country. Apparently you were not taught the elimination method in school.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 19 Helpful 40
  • Question
    How do I work with fractions in solving simultaneous equations using elimination method?
    Donagan
    Top Answerer
    The process is the same as outlined above, except that you would have to clear a fraction when solving for a variable. For example, you may see something like 5x/2 = 10, in which case you would just multiply both sides of that equation by 2 and then divide both sides by 5.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 18 Helpful 30
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Tips

      • You can solve it horizontally as well.
        Thanks
      • Remember that if the unknown terms have the same signs you must subtract and if they have different signs you must add the equations.
        Thanks
      • The easiest of all is the elimination method and fastest as well. It is simple and can be learned much more easily then the other two. It is usually used when the equations have the same variable/unknown term disregarding the sign.
        Thanks
      Show More Tips
      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Submit
      Thanks for submitting a tip for review!
      Advertisement

      You Might Also Like

      How to
      Solve Simultaneous Equations Using Substitution Method
      How to
      Solve Simultaneous Equations Graphically
      How to
      Use an Abacus
      How to
      Calculate Percentages
      The Trachtenberg Method: Learn to Calculate Multi-Digit Numbers Quickly
      How to
      Measure Centimeters
      How to
      Write Numbers in Words
      How to
      Calculate Ratios
      How to
      Calculate Growth Rate
      How to Calculate Percentages on a Calculator
      How to
      Measure Grams
      How to
      Calculate Percentage Increase
      How to
      Calculate Pi
      How to
      Find the Domain of a Function
      Advertisement

      References

      1. ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-math-class-10/section/3.6/primary/lesson/solving-simultaneous-linear-equations-by-elimination/
      2. ↑ https://www.youtube.com/watch?v=O-rrOPPmFgM
      3. ↑ https://www.youtube.com/watch?v=7Ja_H6a8ltY
      4. ↑ https://www.mathsteacher.com.au/year10/ch04_simultaneous/03_elimination_method/elim.htm
      5. ↑ https://www.bbc.co.uk/bitesize/guides/z9y9jty/revision/1
      6. ↑ https://www.bbc.co.uk/bitesize/guides/z9y9jty/revision/1
      7. ↑ https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:systems-of-equations/x2f8bb11595b61c86:solving-systems-elimination/a/elimination-method-review

      About This Article

      Thanks to all authors for creating a page that has been read 117,972 times.

      Reader Success Stories

      • Anonymous

        Jul 27, 2016

        "It helps so much because they are using pictures while explaining, so it was easier to understand."
      Share your story

      Did this article help you?

      Advertisement