The problem consists of a system of linear equations:

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

Solution:

Step 1: Substitute $y = x - 3$ into the first equation

The first equation is $3x - 2y = 6$. Replace $y$ with $x - 3$: $3x - 2(x - 3) = 6$

Step 2: Simplify

Distribute the $-2$ over $(x - 3)$: $3x - 2x + 6 = 6$

Combine like terms: $x + 6 = 6$

Step 3: Solve for $x$

Subtract 6 from both sides: $x = 0$

Step 4: Solve for $y$

Use the second equation, $y = x - 3$, and substitute $x = 0$: $y = 0 - 3$

$y = -3$

Final Answer:

The solution is: $x = 0, \, y = -3$

Would you like a detailed explanation of any step, or is there anything else you'd like to explore?

Related Questions:

1. What is the graphical interpretation of the solution of this system of equations?
2. How do you determine if a system of equations is consistent or inconsistent?
3. Can substitution be replaced with the elimination method here? How?
4. How can we verify the solution using both equations?
5. What is the significance of solving systems of linear equations in real-world applications?

Tip:

When solving a system of equations, always verify the solution by substituting the values back into the original equations.