# How do you solve the system of linear equations -4x+y=2 and 8x-2y=-4?

Mar 21, 2016
1. x = 0
y= 2

2. x = 0
y=2

#### Explanation:

When trying to solve and equation and find the solution for each isolated variable (x, y), always set the opposite of what you are trying to find equal to 0.

Ex. -4x + y = 2 ----> Set x to zero to isolate y
-4(0) + y = 2
Therefore, y =2
Next step, substitute your known value (y) into the original equation and isolate for x.
-4x + y = 2
-4x + 2= 2
Isolate x on one side of the equation (opposite of adding 2 is subtracting 2, to eliminate the variable.)
-4x +2 -2 = 2-2
-4x = 0
Isolate x by itself by dividing (opposite of multiplying by -4 is dividing by -4 ---> Something divided by itself is always 1.)

-4x / -4 = 0 / -4
Therefore, since anything trying to divide into 0 is 0, x = 0

Also, if you have a graphing calculator, you could find the solution to the systems of equations graphically. The point of intersection between the lines of each equation is the solution.