To solve the system of equations by substitution, follow these steps:
Given the system:
[tex]\[
\begin{array}{l}
y = -7x - 11 \\
-4x - 5y = 24
\end{array}
\][/tex]
1. Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[
y = -7x - 11
\][/tex]
Substitute [tex]\( y \)[/tex] in [tex]\(-4x - 5y = 24\)[/tex]:
[tex]\[
-4x - 5(-7x - 11) = 24
\][/tex]
2. Simplify the equation:
[tex]\[
-4x + 35x + 55 = 24
\][/tex]
3. Combine like terms:
[tex]\[
31x + 55 = 24
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
31x = 24 - 55
\][/tex]
[tex]\[
31x = -31
\][/tex]
[tex]\[
x = -1
\][/tex]
5. Substitute [tex]\( x = -1 \)[/tex] back into the first equation to solve for [tex]\( y \)[/tex]:
[tex]\[
y = -7(-1) - 11
\][/tex]
[tex]\[
y = 7 - 11
\][/tex]
[tex]\[
y = -4
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, -4)
\][/tex]
