Well, we know that:
1/2(x) + 1/2(y) = 18
2( 1/2(x) + 1/2(y) ) = 2( 18 )
x + y = 36
and
x - y = 4
if we add y to both sides of x - y = 4, we get x = 4 + y. We can substitute that into our first equation.
4 + y + y = 36
subtract 4 from both sides and add like terms:
2y = 32
Divide both sides by 2:
y = 16
Substitute this into our second equation:
x - 16 = 4
Add 16 to both sides:
x = 20
We can check this by Substituting x with 20 and y with 16:
20 + 16 = 36
It checks out!
x = 20
y = 16
