Let's go through each of the problems step by step:

Question 1: Vocabulary

The pair of numbers $(3, -1)$ is referred to as an ordered pair.

Question 2: Solving for $y$

Given the equation $x + 2y = 8$, we are asked to find the value of $y$ when $x = 3$.

Substitute $x = 3$ into the equation: $3 + 2y = 8$ Now, subtract 3 from both sides: $2y = 8 - 3$ $2y = 5$ Finally, divide both sides by 2: $y = \frac{5}{2} \quad \text{or} \quad y = 2.5$

Question 3: Which equation has $x = -2$ as its solution?

Now we need to determine which of the following equations has $x = -2$ as its solution:

• A: $x - 2 = 0$
• B: $-2 + x = 0$
• C: $2 + x = 0$
• D: $2 - x = 0$

Let’s check each option:

• A: $x - 2 = 0$
  Add 2 to both sides: $x = 2$ So, this does not give $x = -2$.

• B: $-2 + x = 0$
  Add 2 to both sides: $x = 2$ So, this does not give $x = -2$.

• C: $2 + x = 0$
  Subtract 2 from both sides: $x = -2$ This is a match! So, C is the correct answer.

• D: $2 - x = 0$
  Subtract 2 from both sides: $-x = -2$ Multiply both sides by -1: $x = 2$ So, this does not give $x = -2$.

Therefore, the correct answer is C: $2 + x = 0$.

Let me know if you need more detailed explanations or have other questions!

Related Questions:

1. How do you solve a linear equation for a specific variable?
2. What are the differences between an ordered pair and a linear pair?
3. What does it mean to have an equation with a particular solution, such as $x = -2$?
4. How would you graph an ordered pair on a coordinate plane?
5. Can you find the solution for any variable in a multi-variable equation?

Tip: When solving for a variable, always isolate the variable first by performing the inverse operations on both sides of the equation.