The short answer is to solve one equation for one variable, then swap that variable in a different equation.
Example:
2x + 2y = 6
y-x = 1
Step 1: solve either equation for a variable: (#2) y = x+1
Step 2: substitute for your solved variable (I can substitute x+1 for y)
(#1) 2x + 2(x+1) = 6
2x + 2x + 2 = 6
4x + 2 = 6
4x = 4
x = 1
now use x=1 to solve for y in either original equation
