Simplify the following expressions by combining like terms

8x + 7 - 8y + 6x - 8

What is the constant for the variable y after simplification

To simplify the expression \(8x + 7 - 8y + 6x - 8\), let's follow these steps:

### Step 1: Group like terms
1. **Terms with \(x\):** \(8x\) and \(6x\)
2. **Terms with \(y\):** \(-8y\)
3. **Constant terms:** \(7\) and \(-8\)

### Step 2: Combine like terms
1. **Combine \(x\) terms:** 
   \[
   8x + 6x = 14x
   \]
2. **The term with \(y\) stays the same:** \(-8y\)
3. **Combine constant terms:**
   \[
   7 - 8 = -1
   \]

### Final Expression
Combining all the simplified terms, we get:
\[
14x - 8y - 1
\]

Therefore, the constant for the variable \(y\) after simplification is **-8**.

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Would you like more details, or do you have any questions? Here are some related questions you might find interesting:

1. What happens if a term doesn’t have a matching like term?
2. How can you verify if your simplification is correct?
3. What are the rules for adding and subtracting like terms?
4. How can simplification help in solving equations?
5. What is the significance of the coefficients in terms of variable dependency?
6. How do you simplify expressions that include multiplication or division?
7. How can you handle negative coefficients in simplification?
8. Can you explain the distributive property in combining like terms?

**Tip:** Keep an eye on the signs of terms when combining like terms to ensure accuracy.

Learn how to simplify expressions by combining like terms with a step-by-step solution. This problem involves algebraic manipulation and is suitable for Grades 7-9 students.

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