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.