Question

How do you solve `2p+5q=9, 3p-2q=4`?

Answer 1

`p = 38/19` and `q = 1`

Explanation:

`2p + 5q = 9 color(white)(..) ……(1)`
`3p - 2q = 4 color(white)(..) ……(2)`

Multiply equation `(1)` by `2` and equation `(2)` by `5`

`4p + 10q = 18`
`15p - 10q = 20`

Add both the equations

`4p + 10q + 15p - 10q = 18 + 20`

`19p = 38`

`color(blue)(p = 38/19)`

Substitute `p = 38/19` in equation `(1)`

`2(38/19) + 5q = 9`

`76/19 + 5q = 9`

`5q = 9 - 76/19`

`5q = (9 × 19/19) - 76/19`

`5q = 171/19 - 76/19`

`5q = (171 - 76)/19`

`5q = 95/19`

`q = 95/(19 × 5) = 95/95`

`color(blue)(q = 1)`