The system of equations provided is:

$3x + 2y = 0$ $x - 5y = 17$

To solve by elimination, let's eliminate $x$ or $y$. Here’s how:

1. Multiply the second equation by $-3$ to align the $x$-terms for elimination: $3x + 2y = 0$ $-3x + 15y = -51$

2. Now, add these equations together: $(3x - 3x) + (2y + 15y) = 0 + (-51)$ $0 + 17y = -51$ $17y = -51$ $y = -3$

3. Substitute $y = -3$ back into the second original equation: $x - 5(-3) = 17$ $x + 15 = 17$ $x = 2$

Thus, the solution is: $x = 2, \quad y = -3$

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

Follow-Up Questions:

1. How does elimination compare to substitution when solving systems of equations?
2. What are some tips for choosing which variable to eliminate first?
3. How would this solution change if the system had no solution or infinite solutions?
4. Can we verify the solution by substituting the values back into both equations?
5. What are other methods to solve systems of equations, and when are they preferred?

Tip: Always check your solution by plugging it back into the original equations to ensure it satisfies both.