How do you solve linear equations with the substitution method?

For example, you have a system of equations with two variables. You would set one of the  variables (for example, x) in one equation equal to something of the other variable (y). Then you would plug that something of y into the second equation and solve for y. Finally, you would plug in the value you got for y into one of the equations to find x. 

 

Example below: 

y = x + 2

x + y = 12

Plug in (x+2) into the second equation as x:

x + (x+2) = 12

 

Now solve for x:

2x + 2 = 12

2x = 10

x= 5

 

Now plug in 5 for x in the first equation to solve for y:

y = 5 + 2

y = 7