In Parallelogram DEFG, DH= x+3, HF= 3y, GH= 2x-5, and HE= 5y+2. Find the values of x and y.

y=13  , x=36

Step-by-step explanation:

The diagonal of parallelogram bisect at a point where the sides across the intersection are equal

DH=HF

x+3=3y

x=3y-3   first equation

HE=GH

2x-5=5y+2 ⇒ 2x-5y=7 second equation

solve by substitution: x=3y-3

2x-5y=7

2(3y-3)-5y=7

6y-6-5y=7

y=7+6

y=13

x=3y-3

x=3(13)-3

x=36