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:

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.