Question

How do you solve the system of equations `7x - 7y = - 7` and `- 3x + y = 13`?

Answer 1

The answers are `x=-6` and `y=-5`.

Explanation:

You can simplify the first equation:

`7x-7y=-7`

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

`x-y=-1`

Now you can solve for either `x` or `y`, I'll solve for `x` (for no particular reason):

`xcancel(-y color(red)(+y))=-1color(red)(+y)`

`x=-1+y`

Now we plug this `x` into the other given equation and solve for `y`:

`-3x+y=13=>`

`-3(-1+y)+y=13`

`3-3y+y=13`

`3-2y=13`

`-2y=10`

`y=-5`

Finally, plug `y` into either one of the equations to solve for `x`:

`-3x+y=13=>`

`-3x-5=13`

`-3x=18`

`x=-6`

Your final answers are `x=-6` and `y=-5`.