Jack wants to find the solution to a system of equations using y = x + 3 and y = x^2 + 6x - 21. Betty says that Jack can solve x^2 + 5x - 24 = 0 to find the x-coordinates of the solutions of the system. Explain and demonstrate why Betty is correct.

Question

whpalmer4 · Answer

A solution to that system of equations will be a point $(x,y)$ where both equations are true.  If they are true at the same point, then $x$ in one equation equals $x$ in the other equation, and similarly $y$ in one equation equals $y$ in the other.  That means we can say $$y = y$$$$x+3 = x^2+6x-21$$
What do you get when you collect all of the like terms in that equation?

anonymous · Answer

-5x= x^2 - 24?