Solve for a variable in one of the equations and then use that equality to substitute into the other equation.
1st Eq.
-x + y = 5
y = 5 + x
Substitute this in for "y" in 2nd Eq.
2nd Eq.
4x + y = 10
4x + (5+x) = 10
4x + 5 + x = 10
5x + 5 = 10
5x = 10 - 5
5x = 5
x = 5/5
x = 1
