Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?
a(1, 0) and (0, –1)
b(–2, –3) and (1, 0)
c(0, –3) and (1, 0)
d(–3, –2) and (0, 1)

For the solution(s) to exist the equations must be equal to each other.  Thus we can say y=y which means:

x^2+2x-3=x-1  subtract x from both sides

x^2+x-3=-1  add 1 to both sides

x^2+x-2=0  now factor

(x+2)(x-1)=0, so there are two solutions:

x=-2 and 1, to find the corresponding y values we can use y=x-1

y(-2)=-3 and y(1)=0 so the two solutions are the points:

(-2,-3) and (1,0)

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.