Question

How do you solve the system of equations: 5x + 3y = 12 ; 4x - 5y = 17?

Answer 1

The solutions are
`color(blue)(y=-1,x=3`

Explanation:

`5x + 3y = 12`, multiplying by `4`
`color(blue)(20x) + 12y = 48`....equation `1`

`4x - 5y = 17`, multiplying by `5`
`color(blue)(20x) - 25y = 85`.....equation `2`

Solving by elimination

Subtracting equation `1` from `2`

`cancelcolor(blue)(20x) + 12y = 48`
`cancel(-color(blue)(20x)) + 25y = -85`

`37y=-37`
`color(blue)(y=-1`

Finding `x` from equation `1`
`5x + 3y = 12`

`5x = 12-3y`

`5x = 12+3`

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