Ralph wants to find the solution to a system of equations using y = x - 2 and y = x2 + 6x - 38. Joey says that Ralph can solve x2 + 5x - 36 = 0 to find the x coordinates of the solutions to his system. Explain and demonstrate why Joey is correct.

Question

whpalmer4 · Answer

The solution to a system of equations will give the same value of $y$ for the same value of $x$ in all of the equations of the system.  Therefore, at any value of $x$ that is a solution, $$y=x-2=x^2+6x-38$$or$$x-2=x^2+6x-38$$Is it possible to simplify that equation at all?