To determine which ordered pair is a solution to the equation $x + 7y = 17$, we will substitute the values of $x$ and $y$ from each ordered pair into the equation and check whether they satisfy the equation.

1. Check the pair $(10, 1)$:

Substitute $x = 10$ and $y = 1$ into the equation: $10 + 7(1) = 10 + 7 = 17$ Since $10 + 7 = 17$, the pair $(10, 1)$ satisfies the equation.

2. Check the pair $(-4, 3)$:

Substitute $x = -4$ and $y = 3$ into the equation: $-4 + 7(3) = -4 + 21 = 17$ Since $-4 + 21 = 17$, the pair $(-4, 3)$ also satisfies the equation.

Conclusion:

Both pairs $(10, 1)$ and $(-4, 3)$ satisfy the equation $x + 7y = 17$. Therefore, the correct answer is:

Choice C: Both $(10, 1)$ and $(-4, 3)$

Would you like more details or have any questions?

Here are five related questions:

1. How do you solve equations with two variables like $x + 7y = 17$?
2. What is the method for solving systems of linear equations?
3. How can we graph the equation $x + 7y = 17$?
4. What are the properties of linear equations in two variables?
5. How can ordered pairs represent solutions to equations?

Tip: Always substitute the values of $x$ and $y$ into the equation to check if an ordered pair is a solution.