` 6x + 5y = 7x + 3y + 1 = 2 ( x + 6y - 1 )`

Explanation

To solve the equation \( 6x + 5y = 7x + 3y + 1 = 2(x + 6y - 1) \), we can break it down into two separate equations and solve for \( x \) and \( y \).

### Step 1: Set Up the Equations
From the given equation, we can derive two equations:
1. \( 6x + 5y = 7x + 3y + 1 \)
2. \( 7x + 3y + 1 = 2(x + 6y - 1) \)

### Step 2: Simplify the First Equation
Starting with the first equation:
\[ 6x + 5y = 7x + 3y + 1 \]
Rearranging gives:
\[ 6x + 5y - 7x - 3y - 1 = 0 \]
This simplifies to:
\[ -x + 2y - 1 = 0 \]
or:
\[ -x + 2y = 1 \quad \text{(Equation 1)} \]

### Step 3: Simplify the Second Equation
Now, let's simplify the second equation:
\[ 7x + 3y + 1 = 2(x + 6y - 1) \]
Expanding the right side:
\[ 7x + 3y + 1 = 2x + 12y - 2 \]
Rearranging gives:
\[ 7x + 3y + 1 - 2x - 12y + 2 = 0 \]
This simplifies to:
\[ 5x - 9y + 3 = 0 \]
or:
\[ 5x - 9y = -3 \quad \text{(Equation 2)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( -x + 2y = 1 \)
2. \( 5x - 9y = -3 \)

From Equation 1, we can express \( x \) in terms of \( y \):
\[ -x = 1 - 2y \implies x = 2y - 1 \]

### Step 5: Substitute \( x \) in Equation 2
Substituting \( x = 2y - 1 \) into Equation 2:
\[ 5(2y - 1) - 9y = -3 \]
Expanding this gives:
\[ 10y - 5 - 9y = -3 \]
Simplifying:
\[ y - 5 = -3 \implies y = 2 \]

### Step 6: Find \( x \)
Now that we have \( y = 2 \), substitute it back into the expression for \( x \):
\[ x = 2(2) - 1 = 4 - 1 = 3 \]

### Final Answer
Thus, the solution to the equations is:
\[ x = 3, \quad y = 2 \]