Question

How do you solve the system of equations `x=-10+y` and `-6x+8y=22`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for `x`, substitute `-10 + y` for `x` in the second equation and solve for `y`:

`-6x + 8y = 22` becomes:

`-6(-10 + y) + 8y = 22`

`60 - 6y + 8y = 22`

`60 + 2y = 22`

`60 + 2y - color(red)(60) = 22 - color(red)(60)`

`60 - color(red)(60) + 2y = -38`

`0 + 2y = -38`

`2y = -38`

`(2y)/color(red)(2) = -38/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = -19`

`y = -19`

Step 2) Substitute `-19` for `y` in the first equation and calculate `x`:

`x = -10 + y` becomes:

`x = -10 + -19`

`x = -29`

The solution is: `x = -29` and `y = -19` or (-29, -19)