3x-7=x+20 and y+4=y+2 solve for x and y only equation

Let's solve each equation one by one.

### Equation 1: \( 3x - 7 = x + 20 \)

1. First, subtract \( x \) from both sides to get:
   \[
   3x - x - 7 = 20
   \]
   Simplifying, we have:
   \[
   2x - 7 = 20
   \]

2. Next, add 7 to both sides:
   \[
   2x = 27
   \]

3. Finally, divide both sides by 2:
   \[
   x = \frac{27}{2} = 13.5
   \]

### Equation 2: \( y + 4 = y + 2 \)

1. Subtract \( y \) from both sides:
   \[
   4 = 2
   \]

Since \( 4 = 2 \) is a false statement, there is **no solution** for \( y \) in this equation. It means the equation is inconsistent.

### Final Answer:
- \( x = 13.5 \)
- No solution for \( y \)

Would you like details on any of these steps or have any questions?

Here are 5 related questions you might find interesting:

1. How do you solve a system of linear equations?
2. What does it mean when an equation has no solution?
3. How do you solve a quadratic equation?
4. What are the different types of solutions for linear equations?
5. How can you graphically represent the solutions of equations?

**Tip:** Always check your solutions by plugging them back into the original equations to ensure they satisfy all the given conditions.

Learn how to solve linear equations 3x - 7 = x + 20 and y + 4 = y + 2 with a step-by-step solution. Understand the process of simplifying equations, identifying inconsistencies, and determining solutions. Suitable for students in Grades 7-9.

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