Solve for `x` and `y`
`3x+2y=11` and `2x+3y=4`
Also find p if `p=8x+5y`

Answer

To solve the system of equations:

1. **Equations given:**
\[ 3x + 2y = 11 \quad \text{(1)} \]
\[ 2x + 3y = 4 \quad \text{(2)} \]

2. **Make the coefficients of \(x\) the same:**
We can multiply the first equation by 2 and the second equation by 3 to make the coefficients of \(x\) the same:
\[ 2(3x + 2y) = 2(11) \implies 6x + 4y = 22 \quad \text{(3)} \]
\[ 3(2x + 3y) = 3(4) \implies 6x + 9y = 12 \quad \text{(4)} \]

3. **Subtract the equations (3) and (4):**
Now we subtract equation (3) from equation (4):
\[ (6x + 9y) - (6x + 4y) = 12 - 22 \]
This simplifies to:
\[ 5y = -10 \]

4. **Solve for \(y\):**
Dividing both sides by 5:
\[ y = -2 \]

5. **Substitute \(y\) back into one of the original equations to find \(x\):**
We can substitute \(y = -2\) into equation (1):
\[ 3x + 2(-2) = 11 \]
Simplifying this gives:
\[ 3x - 4 = 11 \]
Adding 4 to both sides:
\[ 3x = 15 \]
Dividing by 3:
\[ x = 5 \]

6. **Now, we have the values of \(x\) and \(y\):**
\[ x = 5, \quad y = -2 \]

7. **Find \(p\) using the formula \(p = 8x + 5y\):**
Substitute \(x\) and \(y\) into the equation for \(p\):
\[ p = 8(5) + 5(-2) \]
This simplifies to:
\[ p = 40 - 10 = 30 \]

8. **Final results:**
\[ x = 5, \quad y = -2, \quad p = 30 \]