Abcd is a parallelogram. use a system to find x and y if ab= 6x+30,. bc=2x-5, cd=2y-10, and ad=y-35

Opposite sides of a parallelogram are equal lengths, so ...

... AB = CD

... 6x +30 = 2y -10

and

... BC = AD

... 2x -5 = y -35

The equations can be put in standard form to get

... 3x -y = -20

... 2x -y = -30

Subtracting the second from the first, we get

... x = 10

Solving for y, we have

... y = 2x+30 = 2·10 +30 = 50

The values of x and y are x=10, y=50.

AB = 6x+30 = 90

BC = 2x-5 = 15

a is the best answer choice