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Let's go through the questions one by one:

### A. Find \( x \)
1. \( x + 2 = 0 \)
   - Subtract 2 from both sides:  
     \( x = -2 \)

2. \( x - 3 = 1 \)
   - Add 3 to both sides:  
     \( x = 4 \)

3. \( 2x - 1 = 0 \)
   - Add 1 to both sides and then divide by 2:  
     \( 2x = 1 \)  
     \( x = \frac{1}{2} \)

4. \( 3x + 2 = 5 \)
   - Subtract 2 from both sides and divide by 3:  
     \( 3x = 3 \)  
     \( x = 1 \)

5. \( -x - 5 = 3 \)
   - Add 5 to both sides and multiply by -1:  
     \( -x = 8 \)  
     \( x = -8 \)

### B. Solve for \( y \) in terms of \( x \)

1. \( x + y = 0 \)
   - Subtract \( x \) from both sides:  
     \( y = -x \)

2. \( -x + y = 2 \)
   - Add \( x \) to both sides:  
     \( y = x + 2 \)

3. \( 3x + y - 1 = 0 \)
   - Add 1 to both sides and subtract \( 3x \):  
     \( y = -3x + 1 \)

4. \( -5x + y + 2 = 1 \)
   - Subtract 2 from both sides and add \( 5x \):  
     \( y = 5x - 1 \)

5. \( -x + y - 3 = -4 \)
   - Add 3 to both sides and add \( x \):  
     \( y = x - 1 \)

### C. Solve for \( y \) in terms of \( x \)

1. \( x - y = 1 \)
   - Subtract \( x \) from both sides:  
     \( -y = 1 - x \), multiply by -1:  
     \( y = x - 1 \)

2. \( x + 2y = 4 \)
   - Subtract \( x \) from both sides and divide by 2:  
     \( 2y = 4 - x \)  
     \( y = \frac{4 - x}{2} \)

3. \( -x - y = 2 \)
   - Add \( x \) to both sides and multiply by -1:  
     \( -y = 2 + x \), so \( y = -(2 + x) \), or \( y = -2 - x \)

4. \( 4x + 2y = 6 \)
   - Subtract \( 4x \) from both sides and divide by 2:  
     \( 2y = 6 - 4x \)  
     \( y = 3 - 2x \)

5. \( 6x - 3y = 3 \)
   - Subtract \( 6x \) from both sides and divide by -3:  
     \( -3y = 3 - 6x \), so \( y = \frac{6x - 3}{3} \), or \( y = 2x - 1 \)

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Would you like any detailed explanations for these steps? 

Here are 5 related questions to deepen your understanding:

1. What is the process to solve for one variable in a multi-variable equation?
2. How can you simplify equations before solving for \( x \) or \( y \)?
3. What does it mean to express a variable "in terms of" another variable?
4. How do you handle negative coefficients when solving equations?
5. Can systems of equations always be solved by simple manipulation?

**Tip**: When solving equations, always keep track of operations carefully, especially when dealing with negatives!

Algebra worksheet with multiple problems to solve for x and y in different equations.

This activity focuses on solving linear equations to find x and y, utilizing basic algebraic techniques such as isolating variables and combining expressions. Suitable for students in Grades 7-9.

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