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

We have two equations:

$$y = x-2$$$$y=x^2+6x-38$$

Left side of both equations are identical.  What does that imply about the right side of both equations?

anonymous · Answer

They could be set equal to each other?

whpalmer4 · Answer

Yes!  And what do you get if you do that, and then move everything to the same side of the equals sign?

anonymous · Answer

x-2=x^2+6x-38
 +2             +2
x=x^2+6x-36
-x        -x
0=x^2+5x-36 .. is that right?

whpalmer4 · Answer

Yes.

anonymous · Answer

Okay thank youuu!