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.