Determine the value of y for the system of equations x-3y=4 and 2x+y=8

x - 3y = 4
2x + y = 8

To solve this system using elimination, multiply the entire top equation by -2.

-2(x - 3y = 4)
-2x + 3y = -8

Now add the two equations together.

    -2x + 3y = -8
       2x + y = 8
+___________
        0 + 4y = 0
                y = 0

Substitute 0 for y into either of the original equations.

x - 3y = 4
x - 3(0) = 4
x - 0 = 4
x = 4

Lastly, substitute both values for x and y into both original equations to check work.

x - 3y = 4
4 - 3(0) = 4
4 - 0 = 4
4 = 4

2x + y = 8
2(4) + 0 = 8
8 + 0 = 8
8 = 8

Answer:
y = 0