Solve for x and y :
4x = 17 - `(x - y)/(8)`
`2y + x = 2 + (5y + 2)/(3)`

Answer

To solve the simultaneous equations given by:

1. \( 4x = 17 - \frac{x - y}{8} \)
2. \( 2y + x = 2 + \frac{5y + 2}{3} \)

we will follow these steps:

### Step 1: Simplify the first equation
Starting with the first equation:
\[ 4x = 17 - \frac{x - y}{8} \]
Multiply through by 8 to eliminate the fraction:
\[ 32x = 136 - (x - y) \]
Distributing the negative sign:
\[ 32x = 136 - x + y \]
Rearranging gives:
\[ 32x + x - y = 136 \]
Combining like terms:
\[ 33x - y = 136 \]
This can be labeled as Equation (1):
\[ 33x - y = 136 \quad \text{(Equation 1)} \]

### Step 2: Simplify the second equation
Now, let's simplify the second equation:
\[ 2y + x = 2 + \frac{5y + 2}{3} \]
Multiply through by 3 to eliminate the fraction:
\[ 3(2y + x) = 3 \cdot 2 + (5y + 2) \]
Expanding both sides:
\[ 6y + 3x = 6 + 5y + 2 \]
Combining like terms on the right side:
\[ 6y + 3x = 8 + 5y \]
Rearranging gives:
\[ 6y - 5y + 3x = 8 \]
This simplifies to:
\[ 3x + y = 8 \]
This can be labeled as Equation (2):
\[ 3x + y = 8 \quad \text{(Equation 2)} \]

### Step 3: Add the two equations
Now we have:
1. \( 33x - y = 136 \)
2. \( 3x + y = 8 \)

Adding these two equations:
\[ (33x - y) + (3x + y) = 136 + 8 \]
The \( -y \) and \( +y \) cancel out:
\[ 36x = 144 \]
Dividing both sides by 36:
\[ x = \frac{144}{36} = 4 \]

### Step 4: Substitute \( x \) back into one of the equations
Now substitute \( x = 4 \) back into Equation (2):
\[ 3(4) + y = 8 \]
This simplifies to:
\[ 12 + y = 8 \]
Solving for \( y \):
\[ y = 8 - 12 = -4 \]

### Final Answer
Thus, the solution is:
\[ x = 4, \quad y = -4 \]