Question

For what values of x and y is PQRS a parallelogram?

Answer 1

Answer:

$y =2$

$x =3$

Step-by-step explanation:

Given

The attached parallelogram

Required

Find x and y

Opposite sides are equal

So:

$PQ = SR\ and\ QR = PS$

This gives:

$2y + 3 = y + 5$ -- (1)

$4x - 3 = 4y + 1$ -- (2)

$2y + 3 = y + 5$

Collect like terms

$2y - y= 5 - 3$

$y =2$

$4x - 3 = 4y + 1$

Substitute $y =2$

$4x - 3 = 4 * 2 + 1$

$4x - 3 = 9$

Collect like terms

$4x = 3 + 9$

$4x = 12$

$x =3$