In parallelogram defg, dh = x + 5, hf = 2y, gh = 3x – 1, and he = 5y + 4. find the values of x and y.

The diagonals of a parallelogram bisect each other.

DH = HF and GH = HE

x + 5 = 2y
3x - 1 = 5y + 4

Solve the first equation for x.
x = 2y - 5

Now substitute 2y - 5 for x in the second equation.

3(2y - 5) - 1 = 5y + 4

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute 20 for y in the first original equation.

x + 5 = 2y

x + 5 = 2(20)

x + 5 = 40

x = 35

x = 35 and y = 20