Question

How do you solve the system of equations `-5x - 7y = - 12` and `7x + 6y = - 6`?

Answer 1

See the entire solution process below:

Explanation:

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

`7x + 6y = -6`

`-color(red)(7x) + 7x + 6y = -color(red)(7x) - 6`

`0 + 6y = -color(red)(7x) - 6`

`6y = -color(red)(7x) - 6`

`(6y)/color(red)(6) = (-color(red)(7x) - 6)/color(red)(6)`

`(color(red)(cancel(color(black)(6)))y)/cancel(color(red)(6)) = (-7x)/6 - 6/color(red)(6)`

`y = -7/6x - 1`

Step 2) Substitute `-7/6x - 1` for `y` in the first equation and solve for `x`:

`-5x - 7y = -12` becomes:

`-5x - 7(-7/6x - 1) = -12`

`-5x + (7xx 7/6x) + (7xx 1) = -12`

`-5x + 49/6x + 7 = -12`

`(6/6 xx -5)x + 49/6x + 7 - color(red)(7) = -12 - color(red)(7)`

`-30/6x + 49/6x + 0 = -19`

`19/6x = -19`

`color(red)(6)/color(blue)(19) xx 19/6x = color(red)(6)/color(blue)(19) xx -19`

`cancel(color(red)(6))/cancel(color(blue)(19)) xx color(blue)(cancel(color(black)(19)))/color(red)(cancel(color(black)(6)))x = color(red)(6)/cancel(color(blue)(19)) xx -color(blue)(cancel(color(black)(19)))`

`x = -6`

Step 3) Substitute `-6` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = -7/6x - 1` becomes:

`y = (-7/6 xx -6) - 1`

`y = (-7/color(red)(cancel(color(black)(6))) xx -color(red)(cancel(color(black)(6)))) - 1`

`y = 7 - 1`

`y = 6`

The solution is: `x = -6` and `y = 6` or `(-6, 6)`