To find the solution to the system of linear equations:
[tex]\[
\left\{
\begin{array}{l}
x + 8y = -16 \\
x - 3y = -5
\end{array}
\right.
\][/tex]
We will solve this system step-by-step.
1. Label the equations:
[tex]\[
\begin{aligned}
&\text{Equation (1):} \quad x + 8y = -16 \\
&\text{Equation (2):} \quad x - 3y = -5
\end{aligned}
\][/tex]
2. Eliminate one of the variables:
To eliminate [tex]\(x\)[/tex], we can subtract Equation (2) from Equation (1).
[tex]\[
\begin{aligned}
&(x + 8y) - (x - 3y) = -16 - (-5) \\
&x + 8y - x + 3y = -16 + 5 \\
&11y = -11
\end{aligned}
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[
\begin{aligned}
&11y = -11 \\
&y = \frac{-11}{11} \\
&y = -1
\end{aligned}
\][/tex]
4. Substitute [tex]\(y\)[/tex] back into one of the original equations to find [tex]\(x\)[/tex]:
Using Equation (2):
[tex]\[
\begin{aligned}
&x - 3(-1) = -5 \\
&x + 3 = -5 \\
&x = -5 - 3 \\
&x = -8
\end{aligned}
\][/tex]
5. Write the solution as an ordered pair:
[tex]\[
\boxed{(x, y) = (-8, -1)}
\][/tex]
The solution to the system of equations is [tex]\(x = -8\)[/tex] and [tex]\(y = -1\)[/tex].
