Question

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

Answer 1

Since DH=HF you set x+3=3y 
GH=HE so 4x-5=2y+3 

This gives you a system and I solved by substitution so I got x alone in the first equation-> x=3y-3 
then I plugged this x into the second equation so 

4(3y-3)-5=2y+3 
12y-12-5=2y+3 
12y-17=2y+3 
10y=20 
y=2 

plug y into the first equation to find x 
x=3(2)-3 
x=6-3 
x=3 

c. x=3, y=2