Question

Solve the following system of equations.

3x2 + 30x + 76 = -y
x2+ 10x + 22 = y
A. x = -4, y = -2
B. x = 4, y = 2
C. x = -4, y = 2
D. x = 4, y = -2

Answer 1

After comparing and simplifying the given system of equations, the solutions for x are found to be -3 and -9, which do not match any of the provided options, suggesting a possible error in the question or answer choices.

Step-by-step explanation:

To solve the given system of equations:

1. 3x2 + 30x + 76 = -y
2. x2 + 10x + 22 = y

Since the first equation equals to -y and the second equation equals y, we can set them equal to each other:

3x2 + 30x + 76 = x2 + 10x + 22

Subtracting the second equation from the first, we get:

2x2 + 20x + 54 = 0

Dividing the entire equation by 2, we get:

x2 + 10x + 27 = 0

Using the quadratic formula, we find the roots as:

x = -3, x = -9

These solutions for x do not match any of the options provided, indicating there might have been a mistake in either the provided question or the options given for the answers.