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Let's check if each of the ordered pairs \((x, y)\) is a solution to the equation \(7x - 2y = 13\).

### Step-by-step process:

We'll substitute each \(x\) and \(y\) value from the ordered pairs into the equation and check if the left-hand side equals 13.

1. **For \((3, 4)\):**
   \[
   7(3) - 2(4) = 21 - 8 = 13
   \]
   Yes, this is a solution.

2. **For \((1, -3)\):**
   \[
   7(1) - 2(-3) = 7 + 6 = 13
   \]
   Yes, this is a solution.

3. **For \((-5, 0)\):**
   \[
   7(-5) - 2(0) = -35 + 0 = -35
   \]
   No, this is not a solution.

4. **For \((-2, 5)\):**
   \[
   7(-2) - 2(5) = -14 - 10 = -24
   \]
   No, this is not a solution.

### Final Answer:

| \((x, y)\)     | Is it a solution? |
|----------------|-------------------|
| \((3, 4)\)     | Yes               |
| \((1, -3)\)    | Yes               |
| \((-5, 0)\)    | No                |
| \((-2, 5)\)    | No                |

Would you like further details on how to solve these types of equations?

Here are 5 related questions to practice:
1. What is the general solution for \(7x - 2y = 13\)?
2. How do you graph the equation \(7x - 2y = 13\) on a coordinate plane?
3. Can two ordered pairs be both solutions to a linear equation simultaneously?
4. How do you derive the slope and intercept from the equation \(7x - 2y = 13\)?
5. What is the significance of intercepts in solving linear equations?

**Tip:** When verifying solutions for a linear equation, always simplify both sides of the equation after substitution to see if they are equal.

For each ordered pair, determine whether it is a solution to 7x - 2y = 13.

Check whether given ordered pairs solve the linear equation 7x - 2y = 13 using substitution. The problem includes key concepts of linear algebra and substitution, suitable for students in Grades 8-10.

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