Question

How do you solve the following system: `y = 3x – 12, 3x + 8y = -2`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y`, substitute `3x - 12` for `y` in the second equation and solve for `x`: xx
)3x + 8y = -2# becomes:

`3x + 8(3x - 12) = -2`

`3x + 24x - 96 = -2`

`27x - 96 = -2`

`27x - 96 + color(red)(96) = -2 + color(red)(96)`

`27x - 0 = 94`

`27x = 94`

`(27x)/color(red)(27) = 94/color(red)(27)`

`(color(red)(cancel(color(black)(27)))x)/cancel(color(red)(27)) = 94/27`

`x = 94/27`

Step 2) Substitute `94/27` for `x` in the first equation and calculate `y`:

`y = 3x - 12` becomes:

`y = 3xx94/27 - 12`

`y = 94/9 - 12`

`y = 94/9 - (9/9 xx 12)`

`y = 94/9 - 108/9`

`y = -14/9`

The solution is `x = 94/27` and `y = -14/9` or `(94/27, -14/9)`