The system of equations provided is:

1. $y = 3x + 6$
2. $3y - 2x = 0$

To solve this system using substitution, we'll substitute the expression for $y$ from the first equation into the second equation.

Steps:

1. From the first equation, $y = 3x + 6$, substitute this expression for $y$ into the second equation $3y - 2x = 0$: $3(3x + 6) - 2x = 0$

2. Now expand and simplify: $9x + 18 - 2x = 0$ $7x + 18 = 0$

3. Solve for $x$: $7x = -18$ $x = -\frac{18}{7}$

4. Substitute the value of $x$ into the first equation to find $y$: $y = 3\left(-\frac{18}{7}\right) + 6$ $y = -\frac{54}{7} + 6$ $y = -\frac{54}{7} + \frac{42}{7} = -\frac{12}{7}$

Thus, the solution to the system of equations is: $x = -\frac{18}{7}, \quad y = -\frac{12}{7}$

Would you like further clarification or details about the steps? Here are some related questions to explore:

1. How would you solve a system of equations using elimination instead of substitution?
2. What if the system was inconsistent? How would that affect the solution process?
3. How can you check the solution to a system of equations?
4. What is the geometric interpretation of a system of equations?
5. How does this approach apply to systems involving more than two variables?

Tip: When solving by substitution, always ensure to replace the expression carefully and simplify the equation step by step.