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?

{–2, 1}
{–2, 4}
{–1, 2}
{–1, 4}

Answer 1

Solving from step 3

• -2x+14=x²-3x+12
• x²-3x+2x-2=0
• x²-x-2=0
• (x-2)(x+1)=0
• x=2 or -1

Option C

Answer 2

• C. { - 1, 2}

Explanation:

The first two steps solved and the last step to be performed

Solve the quadratic equation

• x² - 3x + 12 = - 2x + 14
• x² - 3x + 2x + 12 - 14 = 0
• x² - x - 2 = 0
• x² - 2x + x - 2 = 0
• x(x - 2) + (x - 2) = 0
• (x - 2)(x + 1) = 0

• x - 2 = 0 ⇒ x = 2
• x + 1 = 0 ⇒ x = - 1

The solution is:

• { - 1, 2}

Correct choice is C