Solving a System of Linear Equations – Elimination Method

We are given the system of linear equations:

\[
\left\{
\begin{array}{l}
5x + 3y = -4 \\
x - 3y = 10
\end{array}
\right.
\]

We will use the elimination method to solve this system.

Step 1: Align the system of equations

The equations are already in standard form, so we can directly work with them:

\[
\left\{
\begin{array}{l}
5x + 3y = -4 \hspace{1cm} \text{(Equation 1)}\\
x - 3y = 10 \hspace{1cm} \text{(Equation 2)}
\end{array}
\right.
\]

Step 3: Add the two equations

Now, let's add the two equations:
\[
5x + 3y + x - 3y = -4 + 10 \Rightarrow 6x = 6 \Rightarrow x = 1
\]

Substitute \(x\) in the first equation

\[
5(1) + 3y = -4 \Rightarrow 3y = -4 - 5 \Rightarrow 3y = -9 \Rightarrow y = -3
\]