Question

How do you solve the following linear system: # 3x + y = 1 , x + 2y = -4 #?

Answer 1

Original Equations:
`3x+y=1`
`x+2y=-4`

First, you isolate a variable. I chose to set the second equation equal to `y`.

`y=-3x+1`

Next, plug the above equation for `y` into the equation you haven't used yet.
`x+2(-3x+1)=-4`

Multiply it out and combine like terms.
`x-6x+2=-4`
`-5x+2=-4`

Now, solve for `x`
`-5x+22=-4`
`-5x=-6`
`x=6/5`

Plug in `x` to solve for `y.` I'm going to plug it into the equation I used first:
`y=-3x+1`
`y=-3(6/5)+1`
`y=-18/5+1`
`y=-13/5`

The answer is `(6/5, -13/5)`