How to Solve Simultaneous Equations Using Elimination Method

Last Updated: November 28, 2022 References

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

1
Write down both of the equations that you'll need to solve.^{[1]
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- 3x - y = 12
- 2x + y = 13
2
Number the equations. 3x - y = 12 as number one, and 2x + y = 13 as number two.^{[2]
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3
Check if both equations have the same variable/unknown term in them.^{[3]
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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]
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- 3x - y = 12
- + 2x + y = 13
- -------------
- 5x = 25
5
Solve to find the first unknown variable from the resulting (rather shortened) equation. 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]
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6
25 divided by 5 makes 5 so we have now found the value of "x" which is 5.
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]
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- 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]
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- 3x - y = 12
- 3(5) - 3 = 12
- 15 - 3 = 12
- 12 = 12

Community Q&A

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.)
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.
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.