Find the value of x and y that ensure each quadrilateral is a parallelogram.

x = 5, y = 2.

Explanation:

If the figure is a parallelogram then opposite sides are equal and parallel so y = -x + 7 and 2y + 4x = 24.

We can write y = -x + 7 as x + y = 7, so we have:

  x + y = 7          (1)

4x + 2y = 24      (2)

Multiply (1) by 2:

2x + 2y = 14

Subtract this from (2):

2x = 10

x = 5.

So from (1):

5 + y = 7

y = 2.