Question

How do you solve the system of equations: 3x - 4y = -30, 3x+2y=6?

Answer 1

The solutions for the equations are
`color(blue)(x=-2,y=6`

Explanation:

`color(blue)(3x) - 4y = -30`.....equation `1`
`color(blue)( 3x)+2y=6`.............equation `2`

Solving by elimination.

Subtracting equation `2` from `1` results in elimination of `color(blue)(3x`
`cancel(color(blue)(3x)) - 4y = -30`
`-cancel(color(blue)( 3x))-2y=-6`

`-6y=-36`
`color(blue)(y=6`

Now we find `x` by substituting `y` in equation `1`
`3x - 4y = -30`
`3x = -30+4y`
`3x = -30+4*6`
`3x = -30+24`
`3x=-6`
`color(blue)(x=-2`