Solving a System of 2 Equations Using the Addition/Subtraction Method
To solve a system of linear equations using the addition/subtraction method, both equations should first be written in the form Ax + By = C.
Let's take a look at the system of equations below:
x + 2y = 3
15x - 2y = 29
As shown below, adding the equations together eliminates one of the variables. In this case, it's the y-variable that is eliminated.. Now we're left with 16x = 32. Solving for x, we get x = 2.
Substitute 2 for the x-variable in either of the original equations and solve for y. (We'll use the equation x + 2y = 3 because it looks simpler.)
x + 2y = 32+2y = 32y = 1Y = 1/2So we claim that the solution to the system is (2, 1/2) Now check this answer in both of the original equations: Therefore, the solution to the system is (2, 1/2)