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The first step in determining the solution to the system of equations [tex]y = -x^2 - 4x - 3[/tex] and [tex]y = 2x + 5[/tex] algebraically is to set the two equations equal as [tex]-x^2 - 4x - 3 = 2x + 5[/tex].

What is the next step?

A. Set [tex]y = 0[/tex] in [tex]y = -x^2 - 4x - 3[/tex].
B. Factor each side of the equation.
C. Use substitution to create a one-variable equation.
D. Combine like terms onto one side of the equation.

Sagot :

GinnyAnswer
To find the solution to the system of equations given by [tex]\( y = -x^2 - 4x - 3 \)[/tex] and [tex]\( y = 2x + 5 \)[/tex], the first step is to set the two equations equal to each other:

[tex]\[ -x^2 - 4x - 3 = 2x + 5 \][/tex]

The next step is to get all the terms on one side of the equation to set it equal to zero. This involves combining like terms. To do this, we subtract [tex]\( 2x + 5 \)[/tex] from both sides of the equation:

[tex]\[ -x^2 - 4x - 3 - 2x - 5 = 0 \][/tex]

Combining like terms, we obtain:

[tex]\[ -x^2 - 6x - 8 = 0 \][/tex]

So, the correct next step is to combine like terms onto one side of the equation:

[tex]\[ -x^2 - 6x - 8 = 0 \][/tex]
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