Solve for x and y:

3x+2y=11
2x+3y=4

Answer

To solve the system of equations:

1. **Write down the equations:**
\[ 3x + 2y = 11 \quad \text{(Equation 1)} \]
\[ 2x + 3y = 4 \quad \text{(Equation 2)} \]

2. **Multiply the equations to align coefficients for elimination:**
- Multiply Equation 1 by 3:
\[ 3(3x + 2y) = 3(11) \implies 9x + 6y = 33 \quad \text{(Equation 3)} \]
- Multiply Equation 2 by 2:
\[ 2(2x + 3y) = 2(4) \implies 4x + 6y = 8 \quad \text{(Equation 4)} \]

3. **Subtract Equation 4 from Equation 3 to eliminate \(y\):**
\[ (9x + 6y) - (4x + 6y) = 33 - 8 \]
This simplifies to:
\[ 5x = 25 \]

4. **Solve for \(x\):**
\[ x = \frac{25}{5} = 5 \]

5. **Substitute \(x\) back into one of the original equations to find \(y\):**
- Substitute \(x = 5\) into Equation 1:
\[ 3(5) + 2y = 11 \]
This simplifies to:
\[ 15 + 2y = 11 \]
\[ 2y = 11 - 15 \]
\[ 2y = -4 \]
\[ y = \frac{-4}{2} = -2 \]

6. **Final solution:**
The values of \(x\) and \(y\) are:
\[ x = 5, \quad y = -2 \]