# System of Equations Addition Method

by Charles
(Corning, New York )

-2x+5y=1
x-2y=4
The answer in the math book is x=22 y =9
I've been getting a different answer.

Average Rating     Jun 03, 2010 Rating     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: http://www.algebra-class.com/systems-of-equations.html I hope this helps, Karin