Question

For which value of p and q does the following pair of linear equations have an infinite

number of solutions?

2x + 3y = 7

( p-q ) x + (p+q) y = 3 p + q -2

Answer 1

`p =2.5`

`q = 0.5`

Explanation:

Given

`2x + 3y = 7`

`( p-q ) x + (p+q) y = 3 p + q -2`

Required

Find p and q

To do this, we make direct comparison between the given expressions.

`2x + 3y = 7` and
`( p-q ) x + (p+q) y = 3 p + q -2`

This implies that:

`(p - q)x = 2x`

`(p+q)y = 3y`

`3(p + q) - 2 = 7`

So, we have:

`p - q = 2` --- (1)

`p+q =3` -- (2)

`3(p + q) - 2 = 7` --- (3)

If
`(1)\ and\ (2)` are true, then
`(3)\ must` be true.

So, we only solve
`(1)\ and\ (2)`

Add (1) and (2) to eliminate q

`p+p-q+q=2+3`

`2p=5`

Solve for p

`p = 5/2`

`p =2.5`

Substitute
`p =2.5` in (2)

`p+q =3`

`q = 3 - p`

`q = 3 - 2.5`

`q = 0.5`