Since your equations are both of the form y = (something only involving x) then either can be used to substitute for y in the other and you'll get the same thing, namely an equation in x alone. In your example it would be x^2 + 2x - 2 = 3x + 4 which is a quadratic in x. You get two values of x, namely x=-2 and x=3 and the corresponding values of y are then -2 and 13. So the solutions are (x=-2,y=-2) and (x=3,y=13).
You might like to graph the two functions y=x^2+2x-2 and y=3x+4: one is a parabola and the other a straight line. They should intersect in two points, with coordinates giving you the two solutions.