Question

How do you solve the system `8x + 7y = -16` and `6x - 3y = -12`?

Answer 1

`color(red)( x = -2, y=0`

Explanation:

Solving by elimination :

`8x + 7y = -16`
Multiplying the equation by `3` :
`color(red)(24x )+ 21y = -48`...................EQUATION `1`

`6x - 3y = -12`
Multiplying the equation by `4`:
`color(red)(24x) - 12y = -48` ..................EQUATION `2`
The purpose of this multiplication was to create a common term `24x` in both of the equations to enable elimination

Subtracting equation `2` from `1`
`color(red)(24x )+ 21y = -48`
`-color(red)(24x) + 12y = +48`
`0 + 33y =0`
`y = 0`

Finding `x`
`8x = -16 - 7y`
`8x = -16 -0`
`x = -2`