Question

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

Answer 1

`y =2`

`x =3`

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`