Solving a System of Linear Equations – Elimination Method

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
$$5(1) + 3y = -4 \Rightarrow 3y = -4 – 5 \Rightarrow 3y = -9 \Rightarrow y = -3$$

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