Notice -y in the first equation and y in the second equation. If you add -y to y, you get zero, and the y variable is eliminated. We add the equations to use the elimination method and eliminate y.
3x - y = 1
-2x + y = 2
Add equations to get
x = 3
Now that we have x = 3, we substitute 3 for x in the first equation and solve for y.
3(3) - y = 1
9 - y = 1
-y = -8
y = 8
Solution: x = 3; y = 8
