Which ordered pair is a solution of the equation?
\[ x+7y=17\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   Only
\[(10,1)\]
A
Only
\[(10,1)\]
(Choice B)   Only
\[(-4,3)\]
B
Only
\[(-4,3)\]
(Choice C)   Both
\[(10,1)\] and
\[(-4,3)\]
C
Both
\[(10,1)\] and
\[(-4,3)\]
(Choice D)   Neither
D
Neither

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.

Which ordered pair is a solution of the equation?
\[ x + 7y = 17 \]
Choose 1 answer:
(Choice A) Only \( (10,1) \)
(Choice B) Only \( (-4,3) \)
(Choice C) Both \( (10,1) \) and \( (-4,3) \)
(Choice D) Neither

Learn how to determine which ordered pair satisfies the linear equation x + 7y = 17. This step-by-step solution covers key algebraic concepts, including the substitution method in linear equations. Suitable for students in Grades 6-8.

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