To determine if $(1, -3)$ is a solution to the given system of equations:

1. System of equations: 3x - y = 6 \tag{1} 5x + 3y = -4 \tag{2}

2. Substitute $x = 1$ and $y = -3$ into both equations:

   • For Equation (1): $3(1) - (-3) = 3 + 3 = 6$ This satisfies the first equation.

   • For Equation (2): $5(1) + 3(-3) = 5 - 9 = -4$ This satisfies the second equation.

3. Conclusion: Since $(1, -3)$ satisfies both equations, it is a solution to the system.

Would you like a more detailed explanation or have any questions? Here are five related questions for further exploration:

1. How can you graphically verify that $(1, -3)$ lies on both lines represented by the equations?
2. What is the general method for solving systems of linear equations algebraically?
3. What are the possible outcomes (number of solutions) when solving systems of linear equations?
4. How does substitution differ from elimination in solving systems of equations?
5. How can you verify solutions for systems with more than two equations?

Tip: Always substitute the proposed solution into all equations to confirm its validity.