We are given the system of linear equations:

1. $3y + 3 = -5x$
2. $2y - 6 = -2x$

Let's solve this system step by step. I will use the substitution method to find the solution.

Step 1: Solve one equation for one variable

Let's take the second equation: $2y - 6 = -2x$ Add 6 to both sides: $2y = -2x + 6$ Now divide the entire equation by 2: $y = -x + 3$ This is the expression for $y$ in terms of $x$.

Step 2: Substitute into the other equation

Now, substitute $y = -x + 3$ into the first equation: $3y + 3 = -5x$ Substitute $y$ into this: $3(-x + 3) + 3 = -5x$ Simplify: $-3x + 9 + 3 = -5x$ $-3x + 12 = -5x$ Now, add $5x$ to both sides: $2x + 12 = 0$ Subtract 12 from both sides: $2x = -12$ Divide by 2: $x = -6$

Step 3: Solve for $y$

Now that we have $x = -6$, substitute this value into the equation $y = -x + 3$: $y = -(-6) + 3 = 6 + 3 = 9$

Final Solution:

The solution to the system is $x = -6$ and $y = 9$.

Thus, the solution is $(-6, 9)$.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. How can we solve the system using the elimination method?
2. What is the geometric interpretation of the solution of this system of equations?
3. How do we check if the solution is correct by plugging values back into both equations?
4. What are some other methods to solve a system of linear equations?
5. How would the solution change if one of the equations was nonlinear?

Tip: When solving systems of equations, always verify the solution by substituting the values back into the original equations.