Final answer:
Option A presents two distinct equations which can be solved using the substitution method by setting them equal to each other, simplifying, and then applying the quadratic formula to find x, followed by substituting x back into the original equation to find y.
Step-by-step explanation:
The system of equations provided in the question is most likely a misprint since in options B and D, both equations are the same, which means they are either redundant or represent the same line. Let's consider option A where we have two distinct equations: y = -x^2 - 5x - 1, and y = x + 2. We will use the substitution method to solve this system.
Since both equations equal y, we can set them equal to each other:
-x^2 - 5x - 1 = x + 2.
Moving all terms to one side, we get:
x^2 + 6x + 3 = 0.
We can use the quadratic formula to solve for x: x = (-b ± √(b^2 - 4ac)) / (2a). Here, a = 1, b = 6, and c = 3. Plugging in these values gives us two solutions for x.
After finding the x values, we substitute them back into either original equation to find the corresponding y values.