System of Equations Addition Method

by Charles
(Corning, New York )

The answer in the math book is x=22 y =9
I've been getting a different answer.

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Jun 03, 2010
System of Equations Addition Method
by: Karin

Hi Charles,

Here we have a system of equations that you want to solve using linear combinations (aka the addition method).

-2x + 5y = 1
x - 2y = 4

First you need to create one set of opposite terms. I am going to create opposite terms with the x terms by multiplying every term in the 2nd equation by 2. (Remember to multiply all terms, on both sides, by 2)

2(x - 2y) = 4(2)
2x - 4y = 8

So, now we have two equations with opposite terms:
-2x + 5y = 1 (Original equation #1 - left alone
2x - 4y = 8 Equation #2 after multiply by 2)

Now we will add the terms together:
-2x + 5y = 1
2x - 4y = 8
y = 9 (5y - 4y = y & 1 + 8 = 9)

So, now we know that y = 9. Now, we will pick one of the equations and substitute 9 for y and solve for x.

x - 2y = 4
x - 2(9) = 4 (Substitute 9 for y)
x - 18 = 4 (Simplify)
x - 18 +18 = 4 + 18 (Add 18 to both sides)
x = 22

The solution to this system of equations is (22,9)

For more help with solving systems using linear combinations, please visit:

I hope this helps,


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