Question

Find the solution(s) of the system of equations.

y = x² + 4x
y + x² = –4x
a) x=−2,y=0
b) x=0,y=−4
c) x=−4,y=−16
d) x=2,y=0

Answer 1

Main Answer:

The correct solution to the system of equations is option (c) x = -4, y = -16.

Therefore, the correct answer is (c) x = -4, y = -16.

Step-by-step explanation:

The given system of equations is y = x² + 4x and y + x² = -4x. To find the solution, we need to set these two equations equal to each other since they both represent y. By substituting the expression for y from the first equation into the second equation, we get x² + 4x + x² = -4x. Combining like terms, we have 2x² + 4x = -4x. Simplifying further, we get 2x² + 8x = 0. Factoring out a common factor of 2x, we get 2x(x + 4) = 0. This equation is satisfied when either 2x = 0 or (x + 4) = 0. Therefore, the possible values for x are x = 0 or x = -4.

Now that we have the values for x, we can substitute them back into either of the original equations to find the corresponding y-values. Using the first equation y = x² + 4x, if x = 0, then y = 0, and if x = -4, then y = -16. Therefore, the correct solution to the system of equations is x = -4, y = -16.

Therefore, the correct answer is (c) x = -4, y = -16.