Solve this system of equations: y = x2 - 3x + 12 y = - 2x + 14 1. Isolate one variable in the system of equations, if needed. y = x2 - 3x + 12 y = - 2x + 14 2. Use substitution to create a one-variable equation. - 2x + 14 = x2 - 3x + 12 3. Solve to determine the unknown variable in the equation. What are the values of x?

The values of x are 2 and - 1.

Solving the equation created by substitution listed in the question:

-2x+14=x²-3x+12

Add 2x to both sides:

-2x+14+2x=x²-3x+12+2x

14=x²-1x+12

Subtract 14 from both sides:

14-14=x²-1x+12-14

0=x²-1x-2

Factoring this, we want factors of - 2 that sum to - 1; - 2 (1) = - 2 and - 2+1=-1:

0 = (x-2) (x+1)

Using the zero product property, we know that either x-2=0 or x+1=0:

x-2=0

x-2+2=0+2

x=2

x+1=0

x+1-1=0-1

x=-1