Question

How do you solve 5x - 4y = 9 and 3 - 2y = -x?

Answer 1

The solutions are
`color(blue)(x=5,y=4`

Explanation:

`5x - color(blue)(4y) = 9` ......equation `1`

`3 - 2y = -x`
`-x+2y = 3`, multiplying by `2`
`-2x+color(blue)(4y) = 6`.....equation `2`

Solving by elimination
Adding equations `1` and `2`

`5x - cancelcolor(blue)(4y) = 9`
`-2x+cancelcolor(blue)(4y) = 6`

`3x=15`
`color(blue)(x=5`

Substituting `x` in equation `2` to find `y`
`3 - 2y = -x`
`3 +x=2y`
`3 +5=2y`
`y=8/2`
`color(blue)(y=4`