Solve the system of equations: \begin{cases} 6y = 5x - 11, \\ 18y + 35 = 15x. \end{cases}

Solving the system of equations:

We are given the system:

\[ \begin{cases} 6y = 5x - 11, \\ 18y + 35 = 15x. \end{cases} \]

First, we can express the equations as:

\[ \begin{cases} 6y = 5x - 11 \quad (1) \\ 18y = 15x - 35 \quad (2) \end{cases} \]

Multiply equation (1) by 3:

\[ 3(6y) = 3(5x - 11) \implies 18y = 15x - 33 \quad (3) \]

Now we have:

\[ \begin{cases} 18y = 15x - 33 \quad (3) \\ 18y = 15x - 35 \quad (2) \end{cases} \]

Subtract equation (2) from equation (3):

\[ 18y - 18y = (15x - 33) - (15x - 35) \] \[ 0 = 15x - 33 - 15x + 35 \] \[ 0 = 2 \]

This is a contradiction, which means there is no solution to the system of equations. The lines are parallel.

Answer: No solution.