Which of the following equations have x = 2 and y = 1 as a solution?
I.` 2x + 5y = 9`
II. `5x + 3y = 14`
III`2x + 3y = 7`
IV. `2x - 3y = 1`

Options

A. I and IV
B. II and III
C. Only I
D. I, III and IV

Answer

To determine which of the given equations have \( x = 2 \) and \( y = 1 \) as a solution, we will substitute these values into each equation and check if the left-hand side (LHS) equals the right-hand side (RHS).

### Step-by-step Solution:

1. **Equation I: \( 2x + 5y = 9 \)**
- Substitute \( x = 2 \) and \( y = 1 \):
\[ 2(2) + 5(1) = 4 + 5 = 9 \]
- LHS = 9, RHS = 9.
- **Conclusion**: This equation satisfies the condition.

2. **Equation II: \( 5x + 3y = 14 \)**
- Substitute \( x = 2 \) and \( y = 1 \):
\[ 5(2) + 3(1) = 10 + 3 = 13 \]
- LHS = 13, RHS = 14.
- **Conclusion**: This equation does not satisfy the condition.

3. **Equation III: \( 2x + 3y = 7 \)**
- Substitute \( x = 2 \) and \( y = 1 \):
\[ 2(2) + 3(1) = 4 + 3 = 7 \]
- LHS = 7, RHS = 7.
- **Conclusion**: This equation satisfies the condition.

4. **Equation IV: \( 2x - 3y = 1 \)**
- Substitute \( x = 2 \) and \( y = 1 \):
\[ 2(2) - 3(1) = 4 - 3 = 1 \]
- LHS = 1, RHS = 1.
- **Conclusion**: This equation satisfies the condition.

### Summary of Results:
- **Equations that satisfy the condition**: I, III, IV
- **Equation that does not satisfy the condition**: II