How do you solve `3x-y=-4` and `x+3y=-28` using substitution?

One of the variables, either `x` or `y` , must be isolated . In this case, I will rearrange the second equation, `x+3y=-28` and isolate the `x` variable.

`x+3y=-28` Now subtract `3y` from each side of the equation

`x+3y-3y=-28-3y`

`x=-3y-28`

Now that I have isolated the `x` variable in your second equation, I will substitute it in your first equation.

`3x-y=-4`

`3(-3y-28)-y=-4`

`-9y-84-y=-4` collect like terms

`-10y-84 = -4` Add 84 to each side

`-10y-84+84=-4+84`

`-10y=80` Divide by `-10`

`y=-8`
Now simply substitute `-8` in for `y` in either equation.

`x+3y=-28`

`x+3(-8)=-28`

`x-24= -28` Now add `24` to each side of the equation

`x-24+24=-28+24`

`x=-4`

`(-4,-8)`

Now there is one small problem, and that is, how do I know this is the correct solution? Since I used your second equation, `x+3y=-28` to calculate the value of `y`, I can't use this same equation to check my answer. It would always appear to be correct. I must go to the other equation, in your case the first one, to verify that I have the correct answer. So:

`3x-y=-4`

`3(-4)-(-8)=-4`

`-12+8=-4`

`-4=-4`
This confirms that I have the solution correct.