In parallelogram DEFG, DH = x + 2, HF = 2y, GH = 4x – 3, and HE = 5y + 1. Find the values of x and y.

x = 6, y = 4

Step-by-step explanation:

Given the following :

In parallelogram DEFG:

DH = x + 2, HF = 2y, GH = 4x – 3, and HE = 5y + 1

According to the diagram,

The diagonals of the parallelogram buscect each other

The diagonal GE:

GH = HE

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

The Diagonal DF:

DH = HF

x + 2 = 2y

x = 2y - 2 - - - - - (2)

Replace x = 2y - 2 in equation (1)

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

8y - 8 - 3 = 5y + 1

8y - 5y = 1 + 8 + 3

3y = 12

y = 4

Substityte y = 4 in equation (2)

x = 2(4) - 2

x = 8 - 2

x = 6

x = 6, y = 4

practice. practice. practice.