Question

What is the value of x in the following system of equations?

y + 6x = -16
y = x^2 - 7
A) -1
B) 3
C) -3
D) 2

Answer 1

To find the value of x, substitute y from the second equation into the first, simplify and solve the resulting quadratic equation. The correct value of x in the system of equations is -3, which is answer choice C.

Step-by-step explanation:

To find the value of x in the given system of equations, we need to substitute the value of y from the second equation into the first and solve for x. The second equation, y = x2 - 7, can be substituted into the first equation, resulting in x2 - 7 + 6x = -16. We then have a quadratic equation in the form of x2 + 6x + 9 to solve.

While simplifying, we get: x2 + 6x + 9 = 0. This can be factored as (x + 3)2 = 0. Taking the square root of both sides gives us x + 3 = 0, so x = -3.

Therefore, the answer is C) -3.