Solve for x and y
`4(x-3)=3(y+3)`
`17-2x=8-(2y+1)`

Answer

To solve the equations for \( x \) and \( y \), we will follow these steps:

### Step 1: Write down the equations
The equations given are:
1. \( 4(x - 3) = 3(y + 3) \)
2. \( 17 - 2x = 8 - (2y + 1) \)

### Step 2: Simplify the first equation
Start with the first equation:
\[ 4(x - 3) = 3(y + 3) \]
Distributing both sides:
\[ 4x - 12 = 3y + 9 \]
Rearranging gives:
\[ 4x - 3y = 21 \quad \text{(Equation 1)} \]

### Step 3: Simplify the second equation
Now simplify the second equation:
\[ 17 - 2x = 8 - (2y + 1) \]
This simplifies to:
\[ 17 - 2x = 8 - 2y - 1 \]
Which further simplifies to:
\[ 17 - 2x = 7 - 2y \]
Rearranging gives:
\[ 2x - 2y = 10 \quad \text{(Equation 2)} \]
We can simplify this by dividing everything by 2:
\[ x - y = 5 \quad \text{(Equation 2)} \]

### Step 4: Solve the system of equations
Now we have the following system of equations:
1. \( 4x - 3y = 21 \)
2. \( x - y = 5 \)

From Equation 2, we can express \( x \) in terms of \( y \):
\[ x = y + 5 \]

### Step 5: Substitute \( x \) in Equation 1
Substituting \( x \) in Equation 1:
\[ 4(y + 5) - 3y = 21 \]
Expanding gives:
\[ 4y + 20 - 3y = 21 \]
Combining like terms:
\[ y + 20 = 21 \]
Subtracting 20 from both sides:
\[ y = 1 \]

### Step 6: Substitute \( y \) back to find \( x \)
Now substitute \( y = 1 \) back into Equation 2:
\[ x - 1 = 5 \]
Adding 1 to both sides gives:
\[ x = 6 \]

### Final Solution
The solution to the system of equations is:
\[ x = 6, \quad y = 1 \]