To solve the system of equations, let's first rewrite the equations clearly:
- \(3x - 4y = 40\) (Equation 1)
- \(5x - 5y = 55\) (Equation 2)
Let's simplify Equation 2 first. We can divide every term by 5:
\[ x - y = 11 \quad \text{(Equation 2 simplified)} \]
Now we can express \(y\) in terms of \(x\):
\[ y = x - 11 \]
Now we will substitute this expression for \(y\) into Equation 1:
\[ 3x - 4(x - 11) = 40 \]
Expanding this equation:
\[ 3x - 4x + 44 = 40 \]
Combining like terms:
\[ -x + 44 = 40 \]
Now, solve for \(x\):
\[ -x = 40 - 44 \] \[ -x = -4 \] \[ x = 4 \]
Now, substitute \(x = 4\) back into the equation for \(y\):
\[ y = 4 - 11 = -7 \]
So, the solution to the system of equations is:
\[ (x, y) = (4, -7) \]
Thus, the answer is:
\((4, -7)\)