To solve the system of equations:

1. $3x + 2y = -3$
2. $18x + 2y = 12$

We can use elimination or substitution. Here's the solution step by step:

Step 1: Eliminate $y$

Subtract the first equation from the second to eliminate $y$: $(18x + 2y) - (3x + 2y) = 12 - (-3)$ $18x - 3x + 2y - 2y = 12 + 3$ $15x = 15$ $x = 1$

Step 2: Solve for $y$

Substitute $x = 1$ into the first equation: $3(1) + 2y = -3$ $3 + 2y = -3$ $2y = -3 - 3$ $2y = -6$ $y = -3$

Final Solution:

$x = 1, \; y = -3$

Let me know if you'd like further details or if you have additional questions!

Here are 5 questions to expand your understanding:

1. What methods can you use to solve systems of equations?
2. How do you recognize when elimination is the best approach?
3. Can you graphically verify the solution $x = 1, y = -3$?
4. How does substitution differ from elimination in solving systems?
5. What happens if a system has no solution or infinite solutions?

Tip: Always double-check your solution by substituting the values back into the original equations!