Question

The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24, algebraically

are shown in the table.
Step
Equation
Step 1
-x² + 4x + 12 =-3x+24
Step 2
x2 - 7x+12-0
Which represents the solution(s) of this system of equations?
(3, 15)
(-4, 36)
(3, 15) and (4, 12)
(-3, 33) and (-4,36)

Answer 1

(3, 15) and (4, 12)

Explanation:

x2 - 7x+12 = 0 factors to (x - 4)(x - 3) = 0, and so x: {3, 4}.

Since y= -3x + 24, y = 15 when x = 3 and y = 12 when x = 4. The solutions are thus (3, 15) and (4, 12). This is the third answer choice.

Answer 2

see the explanation

Explanation:

Y = –x2 + 4x + 12

y = –3x + 24

so

–x2 + 4x + 12 = –3x + 24

x^2 -7x + 12 = 0

(x - 4)(x - 3) = 0

x - 4 =0; x =4

x - 3 = 0; x= 3

y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)

y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)

answer

(3, 15) and (4, 12)

(give this a heart cause why not)