Question

C D

The first step in determining the solution to the system of equations, y = -x2 - 4x – 3 and y = 2x + 5, algebraical
set the two equations equal as –x2 - 4x - 3 = 2x + 5. What is the next step?
O Set y = 0 in y = -x2 - 4x - 3.
O Factor each side of the equation.
O Use substitution to create a one-variable equation.
O Combine like terms onto one side of the equation.

Answer 1

Combine like terms onto one side of the equation

Step-by-step explanation:

Given the first step in determining the solution to the system of equations,

y = –x2 – 4x – 3 and y = 2x + 5, algebraically as setting the two equations equal as shown: –x2 – 4x – 3 = 2x + 5, the next step will be to combine like terms onto one side of the equation. The like terms are the terms containing the variable x as shown;

-x²-4x-2x = 5+3

As we can see, the term containing x in the right-hand side of the equation (i.e 2x) is being brought to the left side of the equation. This will be the next step in the calculation

Answer 2

Option (4)

Explanation:

Given system of equations is,

y = -x²- 4x - 3

y = 2x + 5

To get the solution of the system of equations algebraically,

2x + 5 = -x²- 4x - 3

Now combine like terms onto one side of the equation.

-x² - (4x + 2x) - (3 + 5) = 0

x² + 6x + 8 = 0

Then factorize the equation,

x² + 4x + 2x + 8 = 0

x(x + 4) + 2(x + 4) =0

(x + 2) (x + 4) = 0

x = -2, 4

Option (4) is the answer.