Question

How do you solve the system of equations `-5x + 3y = 51` and `y = 10x - 8`?

Answer 1

`x=3` and `y=22`

Explanation:

1. `-5x+3y=51`
2. `color(red)(y=10x-8)`

Replace `y` in the first equation with the value of `y` from the second equation which is `color(red)((10x-8))`.

`-5x+3color(red)((10x-8))=51`

Open the brackets and simplify. The product of a positive and a negative is a negative.

`-5x+30x-24=51`

`25x-24=51`

Add `24` to both sides.

`25x=75`

Divide both sides by `25`.

`x=75/25`

`x=3`

Now replace `x` in the second equation with `3`.

`color(red)(y=(10xx3)-8)`

Open the bracket and simplify.

`color(red)(y=30-8)`

`color(red)(y=22)`