You have a system of two linear equations:

1. \(-6x + 3y = -15\)
2. \(4x - 3y = 13\)

To solve this system, you can use either substitution, elimination, or matrix methods. Let's solve it using the **elimination method** by adding the two equations to eliminate \(y\).

### Step-by-step Solution:

1. **Add the equations:**
   \[
   (-6x + 3y) + (4x - 3y) = -15 + 13
   \]
   Simplifying:
   \[
   -2x = -2
   \]

2. **Solve for \(x\):**
   \[
   x = \frac{-2}{-2} = 1
   \]

3. **Substitute \(x = 1\) into one of the original equations.** Let's use the second equation:
   \[
   4x - 3y = 13
   \]
   Substituting \(x = 1\):
   \[
   4(1) - 3y = 13
   \]
   Simplifying:
   \[
   4 - 3y = 13
   \]
   Solving for \(y\):
   \[
   -3y = 13 - 4
   \]
   \[
   -3y = 9 \quad \Rightarrow \quad y = \frac{9}{-3} = -3
   \]

### Final Solution:
- \(x = 1\)
- \(y = -3\)

Would you like more details or have any questions?

### Related Problems:
1. Solve the system: \(2x + y = 5\) and \(3x - y = 4\).
2. Solve the system: \(x - y = 1\) and \(x + y = 9\).
3. Solve the system: \(5x + 2y = 7\) and \(2x - y = 3\).
4. Solve the system: \(x + 2y = 6\) and \(3x - y = 7\).
5. Solve the system: \(7x - y = 4\) and \(5x + 3y = 2\).

### Tip:
When using elimination, aim to cancel one variable by adding or subtracting the equations. This makes solving for the other variable straightforward.

Learn how to solve the system of linear equations -6x + 3y = -15 and 4x - 3y = 13 using the elimination method. This detailed guide walks through each step, making it ideal for students in Grades 8-10 who are studying algebra and systems of equations.

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