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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!

Identify whether the ordered pairs (1,2), (-4,5), (3,-3), (0,6) are solutions to the linear equation 7x - 5y = -3.

Learn how to determine whether the ordered pairs (1,2), (-4,5), (3,-3), and (0,6) are solutions to the linear equation 7x - 5y = -3 using substitution. This algebra problem is ideal for students in Grades 7-9.

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