Answer:
C) {–1, 2}
Step-by-step explanation:
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The solution of the system are { x = 2, y = 10} or { x = -1 , y = 16}
Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
The given system of equations:
y = x² – 3x + 12
y = –2x + 14
Substitute the y = -2x + 14 into the first equation :
–2x + 14 = x² – 3x + 12
Rewrite the equation that all nonzero terms to the left side of the equation,
x² – 3x + 12 + 2x - 14 = 0
Combine the same terms in the equation,
x² - x - 2 = 0
x²- 2x + x - 2 = 0
Factor the first two terms and the last two terms separately
x(x- 2) + 1 (x - 2) = 0
(x - 2)( x+1 ) = 0
Apply Zero Product Property
x - 2 = 0 or x + 1 = 0
Rearrange unknown terms to the left side of the equation:
x = 2 or x = -1
Substitute the value x = 2 into the equation y = –2x + 14,
y = –2(2) + 14
y = –4 + 14
y = 10
Substitute the value x = -1 into the equation y = –2x + 14,
y = -2(-1) + 14
y = 2 + 14
y = 16
Hence, the solution of the system are { x = 2, y = 10} or { x = -1 , y = 16}
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