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
x? - 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)

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)

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

sine

step-by-step explanation: