Find the solutions of the system. y=x^2+3x-4 y=2x + 2, have to show work

Hint: There are several ways to proceed in this kind of problems, but usually the simplest and the one that will yield the most success on average is substituting.

Look at y variable and the expressions to which it is equal; substitute the easier-looking one in the more complicated.
Applying this, we get: 2x+2=x^2+3x-4
x^2+x-6=0.

Solving this equation of 2nd degree, we have a=1, b=1, c=-6 and we get Δ=25 and the solutions are -3 and 2. Hence, we get that the only possible values for x are -3 and 2.
To get the solutions, we have to also find the corresponding y-values:
For x=-3, y=2x+2=-4. For x=2, y=6.

Hence, the 2 pairs of solutions are: (-3,-4) and (2,6)

Main idea on left, details on right