I’m parallelogram defg, dh = x + 3, hf = 3y, gh = 2x - 5, and he = 5y + 2. find the values of x and y.

in parallelogram we know that diagonal are equal in length and intersecting at point

we know that value a diagonal is half the value of itself at intersecting point .

here H is the intersecting point of diagonals.

we know that DF=DH+HF

we know DH=HF

x+3=3y

so x-3y=-3(1)

GE=GH+HE

GH=HE

2x-5=5y+2

2x-5y=7(2)

if we solve equation 1 and 2 by elimination method.

x=36 and y=13.

so, converting firstly the mixed fractions to improper fractions and then "adding".