To solve the given problem, we need to determine whether each ordered pair $(x, y)$ is a solution to the equation $7x - 5y = -3$.

The equation is:

$7x - 5y = -3$

Now, let's test each ordered pair one by one by substituting the values of $x$ and $y$ into the equation and checking if the left-hand side equals $-3$.

1. $(1, 2)$

Substitute $x = 1$ and $y = 2$ into the equation: $7(1) - 5(2) = 7 - 10 = -3$ Yes, this is a solution.

2. $(-4, 5)$

Substitute $x = -4$ and $y = 5$ into the equation: $7(-4) - 5(5) = -28 - 25 = -53$ No, this is not a solution.

3. $(3, -3)$

Substitute $x = 3$ and $y = -3$ into the equation: $7(3) - 5(-3) = 21 + 15 = 36$ No, this is not a solution.

4. $(0, 6)$

Substitute $x = 0$ and $y = 6$ into the equation: $7(0) - 5(6) = 0 - 30 = -30$ No, this is not a solution.

Summary:

• $(1, 2)$ is a solution.
• $(-4, 5)$, $(3, -3)$, and $(0, 6)$ are not solutions.

Would you like more details or explanations about any specific part? Here are five related questions to expand the understanding:

1. How do you verify if an ordered pair is a solution to a linear equation?
2. Can you derive the general form of a linear equation in two variables?
3. What is the geometric interpretation of solutions to a linear equation?
4. How does the substitution method help in solving systems of linear equations?
5. What happens when there are infinitely many solutions to a system of linear equations?

Tip: Always double-check your substitution to avoid small calculation errors that could affect the final result!