Thread: 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

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