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)

see the explanation

Step-by-step 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)

(3, 15) and (4, 12)

Step-by-step 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.