# Math Help - Solving system of equations algebraically?

1. ## Solving system of equations algebraically?

I am trying to solve this system of equations

(y-1)^2=4+x

x+y=-1

This is what I did

y^2-1y-1y-1y+1=4+x
y^2-2y+1=4+x
y^2-2y-3=x

Then I used the quadratic formula to get x=-3

Then plugged that in to x+y=1
I got y=2

Now I am confused because according to my book there are two solutions for this program I found (-3,2)

But I am having trouble finding the other solution?

2. x= -(1+y)
(y-1)^2=4-(1+y)
y^2-2y+1-4+1+y=0
y^2-y-2=0

You continue.

3. Would you have to use the quadratic formula?

4. ## foil

just continuing from above

$\left(y-1\right)^2 = 4 + \left(-1-y\right)$
$y^2 - y -2=0$
$\left(y+1\right)\left(y-2\right)$
so
$y=-1$ and $y=2$
now plug into $x+y=-1$
you get
$x=0$ and $x=-3$
this is 2 graphs intersecting each other at $(-3,2)$ and $(0,-1)$