You are working with the following system of linear equations:

1. $-3x - 3y = 3$
2. $-4x - 3y = -1$

We can solve this using the method of elimination or substitution. Let's use elimination to eliminate $y$.

Step 1: Subtract the two equations to eliminate $y$.

We have: $(-3x - 3y) - (-4x - 3y) = 3 - (-1)$ Simplifying both sides: $-3x - 3y + 4x + 3y = 3 + 1$ The terms involving $y$ cancel out: $x = 4$

Step 2: Substitute $x = 4$ into one of the original equations to find $y$.

Substitute $x = 4$ into the first equation: $-3(4) - 3y = 3$ Simplifying: $-12 - 3y = 3$ Solve for $y$: $-3y = 3 + 12 = 15$ $y = \frac{15}{-3} = -5$

Final Solution:

$x = 4, \quad y = -5$

Would you like a more detailed explanation of any step, or do you have another question? Here are some related questions you might find interesting:

1. How does the substitution method compare to the elimination method for solving systems of linear equations?
2. How can you check if the solution to the system is correct by substituting back into the original equations?
3. What happens if the two equations are parallel? How would you recognize that?
4. Can you solve a system of equations with more than two variables? If so, how?
5. How do you graph a system of linear equations and interpret the solution geometrically?

Tip: Always check your solutions by substituting them back into both original equations to ensure they satisfy both!