Question

How do you solve this system of equations: `-x - y = 6 and - 2x - y = 8`?

Answer 1

See a solution process below:

Explanation:

Step 1) solve the first equation for `x`:

`-x - y = 6`

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

`-x - 0 = 6 +y`

`-x = 6 +y`

`color(red)(-1) xx -x = color(red)(-1)(6 +y)`

`x = (color(red)(-1) xx 6) +(color(red)(-1) xx y)`

`x = -6 +(-y)`

`x = -6 - y`

Step 2) Substitute `(-6 - y)` for `x` in the second equation and solve for `y`;

`-2x - y = 8` becomes:

`-2(-6 - y) - y = 8`

`(-2 xx -6) - (-2 xx y) - y = 8`

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

`12 + 2y - y = 8`

`12 + 2y - 1y = 8`

`12 + (2 - 1)y = 8`

`12 + 1y = 8`

`12 + y = 8`

`12 - color(red)(12) + y = 8 - color(red)(12)`

`0 + y = -4`

`y = -4`

Step 3) Substitute `-4` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = -6 - y` becomes:

`x = -6 - (-4)`

`x = -6 + 4`

`x = -2`

The Solution Is: `x = -2` and `y = -4` or `(-2, -4)`