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To determine which ordered pair makes the equation \( 2x + y = 7 \) true, we will substitute the \( x \) and \( y \) values from each option into the equation and see which one satisfies it.

The equation is:

\[
2x + y = 7
\]

### 1. \( (4, 2) \)
Substitute \( x = 4 \) and \( y = 2 \):
\[
2(4) + 2 = 8 + 2 = 10 \quad (\text{not equal to } 7)
\]
This is **not** a solution.

### 2. \( (1, -5) \)
Substitute \( x = 1 \) and \( y = -5 \):
\[
2(1) + (-5) = 2 - 5 = -3 \quad (\text{not equal to } 7)
\]
This is **not** a solution.

### 3. \( (3, -1) \)
Substitute \( x = 3 \) and \( y = -1 \):
\[
2(3) + (-1) = 6 - 1 = 5 \quad (\text{not equal to } 7)
\]
This is **not** a solution.

### 4. \( (2, 3) \)
Substitute \( x = 2 \) and \( y = 3 \):
\[
2(2) + 3 = 4 + 3 = 7 \quad (\text{equal to } 7)
\]
This is the **correct** solution.

### Conclusion:
The ordered pair \( (2, 3) \) makes the equation \( 2x + y = 7 \) true.

Would you like further details, or do you have any other questions?

Here are five related questions for further exploration:
1. What is the general process for solving linear equations with two variables?
2. How can you graph the equation \( 2x + y = 7 \)?
3. What is the slope-intercept form of the equation \( 2x + y = 7 \)?
4. How would the solution change if the equation were \( 2x + y = 10 \)?
5. What does it mean for an ordered pair to be a solution to an equation?

**Tip:** When solving linear equations with ordered pairs, always substitute values systematically to check for equality.

Which ordered pair makes the equation 2x + y = 7 true?

Learn how to solve the linear equation 2x + y = 7 by finding which ordered pair satisfies the equation. This problem introduces key algebraic concepts such as substitution and solving for ordered pairs. Suitable for students in Grades 6-8.

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