To solve the system of equations:
- \(3x - 4y = 40\)
- \(5x - 5y = 55\)
First, let's simplify the second equation:
\[ 5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 \]
Now, we can substitute \(x\) in the first equation:
Substituting \(x = y + 11\) into the first equation:
\[ 3(y + 11) - 4y = 40 \]
Expanding that,
\[ 3y + 33 - 4y = 40 \] \[ -1y + 33 = 40 \] \[ -1y = 40 - 33 \] \[ -1y = 7 \implies y = -7 \]
Now substituting \(y\) back into \(x = y + 11\):
\[ x = -7 + 11 = 4 \]
So, the solution to the system of equations is:
\[ (x, y) = (4, -7) \]
Thus, the answer is:
\[ \boxed{(4, -7)} \]