Question

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

Answer 1

See the entire solution process below:

Explanation:

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

`x + y = -3`

`x + y - color(red)(y) = -3 - color(red)(y)`

`x + 0 = -3 - y`

`x = -3 - y`

Step 2) Substitute `-3 - y` for `x` in the first equation and solve for `y`:

`-x - y = 4` becomes:

`-(-3 - y) - y = 4`

`3 + y - y = 4`

`3 + 0 != 4`

`3 != 4`

Because `3` is obviously not equal to `4` there is no solution to this problem. This means the equations are for lines which are parallel but are not the same line, therefore there is no place they intersect.