To solve the system of equations given by:
- \(3x - 4y = 40\) (Equation 1)
- \(5x - 5y = 55\) (Equation 2)
First, let's simplify Equation 2:
\[ 5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 \quad \text{(Equation 3)} \]
Now, we can substitute Equation 3 into Equation 1.
Substituting \(x = y + 11\) into Equation 1:
\[ 3(y + 11) - 4y = 40 \]
Distributing:
\[ 3y + 33 - 4y = 40 \]
Combining like terms:
\[ -y + 33 = 40 \]
To isolate \(y\), subtract 33 from both sides:
\[ -y = 7 \implies y = -7 \]
Now that we have \(y\), substitute it back into Equation 3 to find \(x\):
\[ x = y + 11 \implies x = -7 + 11 = 4 \]
So the solution to the system of equations is:
\[ (x, y) = (4, -7) \]
Thus, the correct response is:
\((4, -7)\)