Solve the system of equations...

First set them equil to each other

2x-2=x^2+2x-3

Subtract 2x from each side

-2=x^2-3

Add 3

1=x^2

Take the square root

x=+-1

 

Now plug both values of x into the equation to find y

 

x=1

y=2x-2

Substitute 1 for x

y=2(1)-2

y=2-2

y=0

One of the solitutions is the point (1,0)

 

x=-1

y=2x-2

Substitute -1 for x

y=2(-1)-2

y=-2-2

y=-4

The other solitution is (-1,-4)