Question

How do you solve the system of equations `9x - 4y = - 7` and `7x - 12y = 39`?

Answer 1

`x=-3` and `y=-5`

Explanation:

`9x-4y=-7`
`7x-12y=39`

From the first equation, we derive a value of `(-12y)`.

`9x-4y=-7`

Subtract `9x` from each side.

`-4y=-7-9x`

Multiply all terms by `3`.

`-12y=-21-27x`

In the second equation, substitute `-12y` with `(color(red)(-21-27x))` and simplify.

`7x-12y=39`

`7x-color(red)(21-27x)=39`

`-20x-21=39`

Add `21` to both sides.

`-20x=60`

Divide both sides by `-20`.

`x=-3`

In the first equation, substitute `x` with `color(blue)(-3)` and simplify.

`9x-4y=-7`

`9(color(blue)(-3))-4y=-7`

`-27-4y=-7`

Add `27` to both sides.

`-4y=20`

Divide both sides by `-4`.

`y=-5`