Jack wants to find the solution to a system of equations using y = x + 3 and y = x2 + 6x - 21. Betty says that Jack can solve x2 + 5x - 24 = 0 to find the x-coordinates of the solutions of the system. Explain and demonstrate why Betty is correct.

Question

anonymous · Answer

The intersection of the line $x+3$ and the parabola $x^2+6x-21$ occurs when the x and y coordinates are the same, which means you can set the y's equal to each other:
$$x+3=x^2+6x-21$$
Rearranging, you set equal to zero:
$$x^2+5x-24=0$$