Question

PLEASE HELP ME PICTURES INCLUDED

Answer 1

Two equations given. We have to find the solution sets for the equations.

y = -x²-2x+8 and y = 2x +11

There are 3 steps given. As both equations are equal to y, so we can equate the x parts.

-x²-2x+8 = 2x+11

0 = x²+4x+3

0 = (x+1)(x+3)

Now we have to use zero product property to solve this. If multiplication of two terms equal to 0, we can set each of them equal to 0.

x+1 = 0 , x+3 = 0

When, x+1 =0, by moving 1 to the other side we will get x = -1.

When x+3 =0, by moving 3 to the other side we will get x =-3

Now for the two values of x, we have to find y .

When x = -1, by plugging in the value to the second equation we will get,

y = 2x+11 = 2×(-1)+11 = -2 +11 = 9

So for x =-1, y =9.

The solution set is (-1, 9)

Now when x = -3, by plugging in the value to the second equation we will get,

y = 2x+11 = 2×(-3) +11 = -6+11 = 5

So for x = -3, y = 5

The solution set is (-3,5)

Therefore, the solutions for the system of equations are (-3, 5) and (-1, 9)

So the third option is correct.