To solve this system, we can use substitution.
x + 6y = 61
x = 61 - 6y
Now we substitute into the other equation.
4 (61 - 6y) - 5y = -17
244 - 24y - 5y = -17
244 -29y = -17
29y = 261
y = 9
Now we find x.
x + 6 (9) = 61
x + 54 = 61
x = 7
That means the solution to this system is (7, 9)