Answer:
C. (3,15) and (4, 12)
Step-by-step explanation:
Given the system of linear equations
y = -x² + 4x + 12 and y=-3x + 24
Since both equations represents the variable y, we will equate both of the equations together.
Step 1: Equating both equations together we have;
-x² + 4x + 12 = -3x + 24
-x²+3x+4x+12-24 = 0
-x²+7x-12 = 0
x² -7x+12 = 0
x²-4x-3x+12 = 0
x(x-4)-3(x-4)= 0
x-3(x-4) = 0
x = 3 and 4
Step 2: substitute x = 3 and 4 into any of the equations to get the value of y. Using equation 2
when x = 3, y = -3(3)+24
y = -9+24
y = 15
when x = 4, y = -3(4)+24
y = -12+24
y = 12
The solutions yo the system of equations are (3,15) and (4, 12)
