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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][tex]$y=0$[/tex][/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 :

GinnyAnsweridn
To solve the system of equations algebraically, the next step after setting the two equations equal to each other, [tex]\(-x^2 - 4x - 3 = 2x + 5\)[/tex], is to combine like terms onto one side of the equation.

1. Set the equations equal:
[tex]\(-x^2 - 4x - 3 = 2x + 5\)[/tex].

2. Move all terms to one side:
[tex]\[ -x^2 - 4x - 3 - 2x - 5 = 0 \][/tex]

3. Combine like terms:
[tex]\[ -x^2 - 6x - 8 = 0 \][/tex]

So, combining like terms onto one side results in the quadratic equation:
[tex]\[ -x^2 - 6x - 8 = 0 \][/tex]

This completes the next step in solving the system of equations algebraically.
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