Find the solution of the pair of equations :

`2x+3y=9`
`3x+4y=5`.

Answer

To solve the pair of equations:

1. **Equations Given:**
\[ 2x + 3y = 9 \quad \text{(Equation 1)} \]
\[ 3x + 4y = 5 \quad \text{(Equation 2)} \]

2. **Multiply Equation 1 by 3:**
\[ 3(2x + 3y) = 3(9) \]
\[ 6x + 9y = 27 \quad \text{(Equation 3)} \]

3. **Multiply Equation 2 by 2:**
\[ 2(3x + 4y) = 2(5) \]
\[ 6x + 8y = 10 \quad \text{(Equation 4)} \]

4. **Subtract Equation 4 from Equation 3:**
\[ (6x + 9y) - (6x + 8y) = 27 - 10 \]
\[ 6x + 9y - 6x - 8y = 17 \]
\[ y = 17 \]

5. **Substitute \(y = 17\) back into Equation 1 to find \(x\):**
\[ 2x + 3(17) = 9 \]
\[ 2x + 51 = 9 \]
\[ 2x = 9 - 51 \]
\[ 2x = -42 \]
\[ x = \frac{-42}{2} = -21 \]

6. **Final Solution:**
The solution pair \((x, y)\) is:
\[ (x, y) = (-21, 17) \]