We need to test whether each ordered pair $(x, y)$ is a solution to the given system of equations:

$5x - 3y = 7 \quad \text{(1)}$ $-2x + 7y = 3 \quad \text{(2)}$

Steps to verify:

1. Plug each pair $(x, y)$ into both equations.
2. Check if both equations are satisfied (i.e., both sides of each equation equal).

Let's check each pair one by one.

For $(2, 1)$:

• Equation (1): $5(2) - 3(1) = 10 - 3 = 7$ ✔️
• Equation (2): $-2(2) + 7(1) = -4 + 7 = 3$ ✔️

$(2, 1)$ is a solution.

For $(-4, -9)$:

• Equation (1): $5(-4) - 3(-9) = -20 + 27 = 7$ ✔️
• Equation (2): $-2(-4) + 7(-9) = 8 - 63 = -55 \neq 3$ ❌

$(-4, -9)$ is not a solution.

For $(9, 3)$:

• Equation (1): $5(9) - 3(3) = 45 - 9 = 36 \neq 7$ ❌
• No need to check the second equation.

$(9, 3)$ is not a solution.

For $(-8, 0)$:

• Equation (1): $5(-8) - 3(0) = -40 - 0 = -40 \neq 7$ ❌
• No need to check the second equation.

$(-8, 0)$ is not a solution.

Final table:

Would you like any further explanation or details?

Here are five follow-up questions:

1. How do you solve systems of equations algebraically?
2. What are alternative methods to check solutions (like graphing)?
3. How can you apply substitution to solve this system of equations?
4. What is the geometrical interpretation of solving a system of two linear equations?
5. How would you find the intersection point of these two lines?

Tip: Always check both equations when determining if a point is a solution to a system!