Expert: Scott A Wilson - 11/20/2011

Question
y= x squared-5x-18/ x+3
y= 3x+2

THANKS!

Answer
If the 2nd equation is y = 3x + 2, put that in the 1st and get 3x + 2 = (x² - 5x - 18)/(x+3).
Multiply both sides by x+3 and get (3x+2)(x+3) = x² - 5x - 18.

Now (3x+2)(x+3)  = 3x² + 9x + 2x + 6 = 3x² + 11x + 6, so we have
3x² + 11x + 6 = x² - 5x - 18.

Adding -x² + 5x + 18 to both sides gives 2x² + 16x + 24 = 0.
Dividing by 2 gives x² + 8x + 12 = 0.

This factors into (x+6)(x+2) = 0, socc x+6=0 or x+2=0.
This results in x=-6 or x=-2.

Since y = 3x+2, when x=-6, y = -18+2 = -16 and
when x=-2, y = -6+2 = -4.

To check, the two values for x can each be put in the first equation one at a time.
When x=-6 is input, y should be -16.  When x=-2 is input, y should be -4.