Let's solve the system of equations step by step:

1. First equation: $-2 = 3y + 6$ Subtract 6 from both sides: $-2 - 6 = 3y$ Simplify: $-8 = 3y$ Now, divide both sides by 3: $y = \frac{-8}{3}$

2. Second equation: $3y = -3x$ Divide both sides by 3: $y = -x$

Now we have two expressions for $y$: $y = \frac{-8}{3} \quad \text{and} \quad y = -x$

Equating the two: $\frac{-8}{3} = -x$

Multiply both sides by -1: $\frac{8}{3} = x$

Thus, the solution is: $x = \frac{8}{3}, \quad y = \frac{-8}{3}$

Would you like further clarification or details on the solution?

Here are 5 related questions to consider:

1. How do you solve a system of linear equations with substitution?
2. What is the significance of the slope in the equation $y = -x$?
3. Can this system of equations be solved using elimination?
4. What is the graphical representation of the system?
5. How do fractions in the solution affect interpretation in real-life contexts?

Tip: When solving equations with fractions, it's often easier to clear the fractions early by multiplying both sides by the denominator.