To solve the system of equations, we can use the substitution method.
First, we use the second equation to express x in terms of y:
x = 5y - 1.
Then, we substitute this expression into the first equation to solve for y:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -16/16
y = -1.
Now that we have found the value of y, we can substitute it back into the second equation to find x:
x = 5(-1) - 1
x = -5 - 1
x = -6.
Therefore, the solution to the system of equations is (x, y) = (-6, -1).