How to Solve Simultaneous Equations Using Elimination Method

Reviewed by Joseph Meyer

Last Updated: February 3, 2025 Fact Checked

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

Download Article

1
Write down both of the equations that you'll need to solve.^{[1]
X
Research source}
- 3x - y = 12
- 2x + y = 13
3x - y = 12 as number one, and 2x + y = 13 as number two.^{[2]
X
Research source}

Advertisement
^{[3]
X
Research source}
4
Look for signs of the unknown variables or terms. 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]
X
Research source}
- 3x - y = 12
- + 2x + y = 13
- -------------
- 5x = 25
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]
X
Research source}
7
Find the value of "y". 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]
X
Research source}
- 3x - y = 12
- 3(5)-y = 12
- 15 - y = 12
- - y = 12 - 15
- - y = - 3(divide both sides by negative one, will be able to cut both signs)
- y = 3
8
Check the problem. 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]
X
Research source}
- 3x - y = 12
- 3(5) - 3 = 12
- 15 - 3 = 12
- 12 = 12

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 19 Helpful 42
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 21 Helpful 44
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 20 Helpful 32

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Tips

You can solve it horizontally as well.

Thanks
Helpful 0 Not Helpful 1
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
Helpful 2 Not Helpful 0
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
Helpful 0 Not Helpful 0