Answer: b. (-5, 8) and (-1, 0)
Step-by-step explanation:
To find the solutions of the system, we can set the two equations equal to each other.
So, we have: x^2 + 4x + 3 = -2x - 2
Rearranging and combining like terms: x^2 + 6x + 5 = 0
Now we can solve for x by factoring the quadratic equation: (x + 5)(x + 1) = 0
Setting each factor equal to zero: x + 5 = 0 --> x = -5 x + 1 = 0 --> x = -1
So, the solutions for x are x = -5 and x = -1.
To find the corresponding y-values, we can substitute these x-values into one of the original equations. Let's use y = x^2 + 4x + 3.
When x = -5: y = (-5)^2 + 4(-5) + 3 y = 25 - 20 + 3 y = 8
When x = -1: y = (-1)^2 + 4(-1) + 3 y = 1 - 4 + 3 y = 0
Therefore, the solutions for the system are (-5, 8) and (-1, 0), which matches with option b. So, the correct answer is:
b. (-5, 8) and (-1, 0)