Question

How do you solve the system of equations `-3x - 4y = - 8` and `2x + y = 12`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for `y`:

`2x + y = 12`

`-color(red)(2x) + 2x + y = -color(red)(2x) + 12`

`0 + y = -2x + 12`

`y = -2x + 12`

Step 2) Substitute `-2x + 12` for `y` in the first equation and solve for `x`:

`-3x - 4y = -8` becomes:

`-3x - 4(-2x + 12) = -8`

`-3x - (4 xx -2x) - (4 xx 12) = -8`

`-3x - (-8x) - 48 = -8`

`-3x + 8x - 48 = -8`

`(-3 + 8)x - 48 + color(red)(48) = -8 + color(red)(48)`

`5x - 0 = 40`

`5x = 40`

`(5x)/color(red)(5) = 40/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 8`

`x = 8`

Step 3) Substitute `8` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = -2x + 12` becomes:

`y = (-2 xx 8) + 12`

`y = -16 + 12`

`y = -4`

The solution is: `x = 8` and `y = -4` or `(8, -4)`