Question

How do you find the exact solutions to the system `y=x+2` and `y=x^2`?

Answer 1

I got:
`(2,4)`
`(-1,1)`

Explanation:

We can substitute the first equation into the second for `y`:
`x+2=x^2`
rearrange and solve for `x` using the Quadratic Formula:
`x^2-x-2=0`
`x_(1,2)=(1+-sqrt(1+8))/2=(1+-3)/2`
giving:
`x_1=4/2=2`
`x_2=-2/2=-1`
that substituted into the original first equation give:
`y_1=2+2=4`
`y_2=-1+2=1`

Graphically: