To solve the system of equations:

\[
\begin{aligned}
1) & \ 3x + 2y = 7 \\
2) & \ x - 3y = 4 
\end{aligned}
\]

We can use either the substitution method or the elimination method. Let's use the elimination method here.

### Step 1: Multiply the second equation by 3 to align the coefficients of \( x \) for elimination.
\[
3(x - 3y) = 3(4)
\]
This gives us:
\[
3x - 9y = 12
\]

### Step 2: Subtract the first equation from this result.
\[
(3x - 9y) - (3x + 2y) = 12 - 7
\]
Simplifying this:
\[
-11y = 5
\]
So, \( y = \frac{-5}{11} \).

### Step 3: Substitute \( y = \frac{-5}{11} \) into the second original equation to solve for \( x \).
\[
x - 3\left(\frac{-5}{11}\right) = 4
\]
Simplifying:
\[
x + \frac{15}{11} = 4
\]
Multiply both sides by 11 to eliminate the fraction:
\[
11x + 15 = 44
\]
So, \( x = \frac{29}{11} \).

### Final Answer:
\[
x = \frac{29}{11}, \quad y = \frac{-5}{11}
\]

Do you want details on any step or have any questions?

Here are 5 related questions:
1. How would you solve the system using the substitution method?
2. Can you graphically interpret the solution to this system?
3. How can we verify that the solution is correct?
4. What happens if the coefficients in the equations were slightly changed?
5. How do you solve a system of equations with three variables?

**Tip:** When solving systems of linear equations, ensure that the method chosen is the most efficient based on the structure of the equations.

Learn how to solve the system of equations 3x + 2y = 7 and x - 3y = 4 using the elimination method. This problem covers systems of linear equations and the step-by-step process to find the solution. Suitable for high school students.

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