To solve this problem, we need to check whether each ordered pair $(x, y)$ satisfies the equation $2x - 7y = -11$. For each ordered pair, we will substitute the values of $x$ and $y$ into the equation and check if the left-hand side equals the right-hand side (-11).

Let's go through the process for each pair:

1. For $(-3, 4)$: $2(-3) - 7(4) = -6 - 28 = -34 \quad (\text{not equal to } -11)$ Therefore, $(-3, 4)$ is not a solution.

2. For $(8, -2)$: $2(8) - 7(-2) = 16 + 14 = 30 \quad (\text{not equal to } -11)$ Therefore, $(8, -2)$ is not a solution.

3. For $(5, 3)$: $2(5) - 7(3) = 10 - 21 = -11 \quad (\text{equals } -11)$ Therefore, $(5, 3)$ is a solution.

4. For $(-1, -5)$: $2(-1) - 7(-5) = -2 + 35 = 33 \quad (\text{not equal to } -11)$ Therefore, $(-1, -5)$ is not a solution.

Summary:

• $(-3, 4)$: No
• $(8, -2)$: No
• $(5, 3)$: Yes
• $(-1, -5)$: No

Would you like any further details or clarification?

Related Questions:

1. What does it mean for an ordered pair to be a solution to a linear equation?
2. How do we graphically interpret the solutions to the equation $2x - 7y = -11$?
3. How can we determine the solution to a linear equation without testing multiple points?
4. What are some methods to solve a system of linear equations algebraically?
5. How would you solve the equation if additional pairs were provided?

Tip:

Always substitute the values of $x$ and $y$ carefully into the equation to ensure accuracy when checking for solutions.