Question

How do you solve the system of equations `7x - 3y = - 65` and `2x + y = - 39`?

Answer 1

See the entire solution process below:

Explanation:

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

`2x + y = -39`

`-color(red)(2x) + 2x + y = -color(red)(2x) - 39`

`0 + y = -2x - 39`

`y = -2x - 39`

Step 2) Substitute `-2x - 39` for `y` in the first equation and solve for `x`:

`7x - 3y = -65` becomes:

`7x - 3(-2x - 39) = -65`

`7x + (3 xx 2x) + (3 xx 39) = -65`

`7x + 6x + 117 = -65`

`13x + 117 = -65`

`13x + 117 - color(red)(117) = -65 - color(red)(117)`

`13x + 0 = -182`

`13x = -182`

`(13x)/color(red)(13) = -182/color(red)(13)`

`(color(red)(cancel(color(black)(13)))x)/cancel(color(red)(13)) = -14`

`x = -14`

Step 3) Substitute `-14` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = -2x - 39` becomes:

`y = (-2 xx -14) - 39`

`y = 28 - 39`

`y = -11`

The solution is: `x = -14` and `y = -11` or `(-14, -11)`