If a = 3x - 5y, b = 6x + 3y` and `c = 2y - 4x`.
Find : (i)`a + b - c`, (ii) `2a - 3b + 4c`.

Answer

To solve the problem, we will find the expressions for (i) \( a + b - c \) and (ii) \( 2a - 3b + 4c \) step by step.

### Given:
- \( a = 3x - 5y \)
- \( b = 6x + 3y \)
- \( c = 2y - 4x \)

### (i) Finding \( a + b - c \)

1. **Write the expression**:
\[ a + b - c = (3x - 5y) + (6x + 3y) - (2y - 4x) \]

2. **Distribute the negative sign**:
\[ = 3x - 5y + 6x + 3y - 2y + 4x \]

3. **Combine like terms**:
- Combine the \( x \) terms: \( 3x + 6x + 4x = 13x \)
- Combine the \( y \) terms: \( -5y + 3y - 2y = -4y \)

4. **Final result**:
\[ a + b - c = 13x - 4y \]

### (ii) Finding \( 2a - 3b + 4c \)

1. **Write the expression**:
\[ 2a - 3b + 4c = 2(3x - 5y) - 3(6x + 3y) + 4(2y - 4x) \]

2. **Distribute the coefficients**:
\[ = (6x - 10y) - (18x + 9y) + (8y - 16x) \]

3. **Combine like terms**:
- Combine the \( x \) terms: \( 6x - 18x - 16x = -28x \)
- Combine the \( y \) terms: \( -10y - 9y + 8y = -11y \)

4. **Final result**:
\[ 2a - 3b + 4c = -28x - 11y \]

### Summary of Results:
- (i) \( a + b - c = 13x - 4y \)
- (ii) \( 2a - 3b + 4c = -28x - 11y \)