Dh = x + 2, hf = 2y, gh = 3x – 3, and he = 5y + 1. find the values of x and y.

DH = x + 2, HF = 2y, GH = 3x – 3, and HE = 5y + 1

DH = HF
x + 2 = 2y
and
GH = HE
3x – 3 = 5y + 1

so now you have
x + 2 = 2y
3x – 3 = 5y + 1

re-write and simply
x = 2y - 2
3x = 5y + 4

substitute x = 2y - 2 into 3x = 5y + 4
3x = 5y + 4
3(2y - 2) = 5y + 4
6y - 6 = 5y + 4
y = 10

x = 2y - 2
x = 2(10) - 2
x = 20 - 2
x = 18

answer
x = 18 and y = 10