Question

How do you solve the system -2x + 2y= -5 and x + y= -5?

Answer 1

`x = -5/4`, `" "y = -15/4`

Explanation:

Eq1: `-2x + 2y = -5`
Eq2: `x+y=-5`

We need to find one of the variables. Since Eq2 already has variables with coefficients of `1`, let's start there. Let's solve for `x` in Eq2:

Eq3: `x = -y-5`

Now we can use Eq3 by substituting it into Eq1. We cannot substitute into Eq2, as we have already used this equation to derive a result!

Eq3 -> Eq1:
`-2(-y-5)+2y=-5`
`=>2y+10+2y=-5`
`=>4y + 10 = -5`
`=>4y = -15`
`=> color(blue)(y = -15/4)`

We now have a value for `y`. We have both Eq1 and Eq2 that must hold. We can use whichever one, as both will give the same results. Let's just substitute into Eq2 for convenience:

`x+(color(blue)(-15/4))=-5`
`=> color(orange)(x = -5/4)`

Now we have values for both `x` and `y`:
`x = -5/4`,`" " y = -15/4`