Solve the system of equations: 6y=5x-11, 18y+35=15x.

First, let's rewrite the equations to have the same form:

$$6y = 5x - 11$$ $$18y + 35 = 15x$$

We can multiply the first equation by 3 to eliminate (y):

$$3(6y) = 3(5x - 11)$$ $$18y = 15x - 33$$

Now we have the system:

$$18y = 15x - 33$$ $$18y = 15x - 35$$

Since both equations are equal to (18y), we can set them equal to each other:

$$15x - 33 = 15x - 35$$

Subtract (15x) from both sides:

$$-33 = -35$$

This is a contradiction, which means the system has no solution.

Answer: No solution