Question

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?

Answer 1

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

Answer 2

Explanation: