https://file.aiquickdraw.com/mathbot/file/172721380856621iojiyv.jpg

The system of equations provided in the image is:

\[
\begin{aligned}
1.\quad & 3x + 3y = 12 \\
2.\quad & x - 3y = -4
\end{aligned}
\]

We are tasked with using the elimination method to solve for \( x \) and \( y \).

### Step 1: Eliminate one variable
To eliminate \( y \), we can add the two equations. This is because the coefficients of \( y \) in the two equations are opposites (i.e., \( +3y \) and \( -3y \)).

\[
(3x + 3y) + (x - 3y) = 12 + (-4)
\]

Simplifying:

\[
3x + x + 3y - 3y = 12 - 4
\]
\[
4x = 8
\]

### Step 2: Solve for \( x \)
\[
x = \frac{8}{4} = 2
\]

### Step 3: Substitute \( x = 2 \) into one of the original equations
We can substitute this value of \( x \) into the second equation \( x - 3y = -4 \):

\[
2 - 3y = -4
\]

### Step 4: Solve for \( y \)
\[
-3y = -4 - 2
\]
\[
-3y = -6
\]
\[
y = \frac{-6}{-3} = 2
\]

### Solution:
The solution to the system of equations is:

\[
(x, y) = (2, 2)
\]

Would you like more details on any step or further clarification? 

Here are 5 related questions to explore further:
1. How does the elimination method work with different coefficients?
2. What if the system had no solution? How would you detect that?
3. How does substitution differ from elimination in solving systems?
4. Can we graphically verify the solution \( (x, y) = (2, 2) \)?
5. What happens if the system has infinitely many solutions?

**Tip:** Always check your solution by substituting the values back into both original equations to ensure correctness.

Use the elimination method to find all solutions of the system of equations: 3x + 3y = 12 and x - 3y = -4.

Learn how to solve the system of linear equations 3x + 3y = 12 and x - 3y = -4 using the elimination method. This step-by-step guide walks through simplifying the system and solving for x and y, suitable for students in Grades 8-10.

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