Question

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In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The diagram is not drawn to scale.

A.x = 6; y =3
B.x = 2; y = 3
C.x = 3; y = 2
D.x = 3; y = 6

Answer 1

alright i think the 2 lines that interesect the parallelogram are both equal so you can set 3y and x+3 equal and you can set 4x-5 and 2y+3 equal so it will look like this

4x-5=2y+3 and 3y=x+3 now we want to solve for one variable so for 3y=x+3 we shall solve for y so we divide the whole thing by 3 so it equals y=x/3+1 now since we have a y value we plug it in into the other equation like this 4x-5=2(x/3+1)+3 which when you solve everything x=3 then you plug in x=3 into anyone of the original equations to find y so we do that whi 3y=x+3 and we and it becomes 3y=6 so y=2. So your answer is C. x=3,y=2

Hope this explanation helped if you have any questions just ask