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The given equation is \( 3x + y = -21 \), and the table asks for ordered pairs \((x, y)\) that satisfy this equation.

### Step-by-step solution:

1. **When \( x = 0 \):**
   - Substitute \( x = 0 \) into the equation:
   \[
   3(0) + y = -21 \implies y = -21
   \]
   - The ordered pair is \( (0, -21) \), which is already filled in the table.

2. **When \( x = 1 \):**
   - Substitute \( x = 1 \) into the equation:
   \[
   3(1) + y = -21 \implies 3 + y = -21 \implies y = -21 - 3 = -24
   \]
   - The ordered pair is \( (1, -24) \).

3. **When \( y = 0 \):**
   - Substitute \( y = 0 \) into the equation:
   \[
   3x + 0 = -21 \implies 3x = -21 \implies x = \frac{-21}{3} = -7
   \]
   - The ordered pair is \( (-7, 0) \).

### Final Answer:
- For \( x = 0 \), \( y = -21 \), so the ordered pair is \( (0, -21) \) (already given).
- For \( x = 1 \), \( y = -24 \), so the ordered pair is \( (1, -24) \).
- For \( y = 0 \), \( x = -7 \), so the ordered pair is \( (-7, 0) \).

Let me know if you'd like more details or have any other questions!

### Related questions:
1. How can you find solutions for other linear equations like \( 2x - 5y = 10 \)?
2. What is the graphical representation of the equation \( 3x + y = -21 \)?
3. How do you solve a linear equation for a different variable, say \( y = mx + c \)?
4. How would the solution table change if the equation were \( 3x - y = -21 \)?
5. What is the slope of the line represented by the equation \( 3x + y = -21 \)?

### Tip:
When solving linear equations, substituting simple values like \( x = 0 \) or \( y = 0 \) helps to quickly find intercepts, which are useful for graphing.

Complete the table below to find solutions to the linear equation 3x + y = -21.

Solve the linear equation 3x + y = -21 by completing the table with ordered pairs. Learn how to substitute values for x and y to find the correct solutions. This problem covers key algebraic concepts for students in Grades 6-8.

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