We have a system of equations that we can solve step-by-step. The system is:

1. \( 3x = 30 \)
2. \( x + 2y = 18 \)
3. \( x - y = 2 \)

### Step 1: Solve for \( x \) from the first equation
From \( 3x = 30 \), divide both sides by 3:

\[
x = \frac{30}{3} = 10
\]

### Step 2: Substitute \( x = 10 \) into the other two equations
Now substitute \( x = 10 \) into the second and third equations.

For \( x + 2y = 18 \):
\[
10 + 2y = 18
\]
Subtract 10 from both sides:
\[
2y = 8
\]
Divide by 2:
\[
y = 4
\]

For \( x - y = 2 \):
\[
10 - y = 2
\]
Subtract 10 from both sides:
\[
-y = -8
\]
Multiply by \(-1\):
\[
y = 8
\]

### Step 3: Conclusion
We found \( y = 4 \) from one equation and \( y = 8 \) from another, but these values contradict each other. This suggests that the system of equations is inconsistent and has no solution.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve systems of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. Can you explain what makes a system of equations inconsistent?
4. How do we identify a system of equations with infinite solutions?
5. How can you graphically represent the solution to a system of equations?

**Tip**: Always double-check the consistency of your equations before solving them to ensure that they don’t contradict each other.

This problem involves solving a system of linear equations using substitution. It demonstrates the concept of inconsistent systems, where no solution exists. The step-by-step guide is ideal for students in Grades 8-10 learning about linear equations.

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