To solve the given system of equations algebraically, follow these steps:
1. Set the two equations equal to each other:
Since we have two equations [tex]\( y = -x^2 - 4x - 3 \)[/tex] and [tex]\( y = 2x + 5 \)[/tex], we start by setting them equal:
[tex]\[
-x^2 - 4x - 3 = 2x + 5
\][/tex]
2. Combine like terms onto one side of the equation:
To create a standard form of a quadratic equation, we need to move all terms to one side of the equation. Subtract [tex]\( 2x + 5 \)[/tex] from both sides:
[tex]\[
-x^2 - 4x - 3 - 2x - 5 = 0
\][/tex]
3. Simplify the equation:
Combine like terms (terms involving [tex]\( x \)[/tex] and constant terms) on the left side of the equation:
[tex]\[
-x^2 - 4x - 3 - 2x - 5 \implies -x^2 - 6x - 8
\][/tex]
This results in:
[tex]\[
-x^2 - 6x - 8 = 0
\][/tex]
Hence, the next step after setting the two equations equal to each other is to combine like terms onto one side of the equation, resulting in [tex]\(-x^2 - 6x - 8 = 0\)[/tex].
