Given the system of linear equations, solve for \(x\) and \(y\):
\[
\left\{
\begin{array}{l}
5x + 3y = -4 \\
x – 3y = 10
\end{array}
\right.
\]
Solution
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
\[
5(1) + 3y = -4 \Rightarrow 3y = -4 – 5 \Rightarrow 3y = -9 \Rightarrow y = -3
\]
\[
x = 1, y = -3 \text{ are the solutions to the system of equations.}
\]
x = 1, y = -3 \text{ are the solutions to the system of equations.}
\]
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