Add the two equations to eliminate y.

(x + y) + (4x - y) = (15) + (20)

5x = 35 (collect terms)

x = 7 (divide by 5)

Subtract 4 times the first equation from the second equation to eliminate x.

(4x - y) - 4(x + y) = (20) - 4(15)

-5y = -40 (collect terms)

y = 8 (divide by -5)

7 + y = 15 (substitute the value of x into the first equation)

y = 8 (subtract 7 from both sides)

(x + y) + (4x - y) = (15) + (20)

5x = 35 (collect terms)

x = 7 (divide by 5)

Subtract 4 times the first equation from the second equation to eliminate x.

(4x - y) - 4(x + y) = (20) - 4(15)

-5y = -40 (collect terms)

y = 8 (divide by -5)

##### The solution is (x, y) = (7, 8).

After you have a value for one of the variables, it is often more convenient to solve for the other using substitution.7 + y = 15 (substitute the value of x into the first equation)

y = 8 (subtract 7 from both sides)