If x has a remainder of 4 when divided by 9 and y has a remainder of 3 when divided by 9, what's the remainder when `x+y` is divided by 9?

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Remainders**:
- We know that when \( x \) is divided by 9, it leaves a remainder of 4. This can be expressed mathematically as:
\[ x = 9a + 4 \]
where \( a \) is some integer (the quotient when \( x \) is divided by 9).

2. **Expressing \( y \)**:
- Similarly, when \( y \) is divided by 9, it leaves a remainder of 3. This can be expressed as:
\[ y = 9b + 3 \]
where \( b \) is another integer (the quotient when \( y \) is divided by 9).

3. **Adding \( x \) and \( y \)**:
- Now, we want to find \( x + y \):
\[ x + y = (9a + 4) + (9b + 3) \]
- Simplifying this, we combine like terms:
\[ x + y = 9a + 9b + 4 + 3 = 9a + 9b + 7 \]

4. **Factoring Out 9**:
- We can factor out 9 from the first two terms:
\[ x + y = 9(a + b) + 7 \]

5. **Finding the Remainder**:
- When \( x + y \) is divided by 9, the term \( 9(a + b) \) will contribute a quotient, and the remainder will be the constant term left, which is 7.
- Therefore, the remainder when \( x + y \) is divided by 9 is:
\[ \text{Remainder} = 7 \]

### Final Answer:
The remainder when \( x + y \) is divided by 9 is **7**.