To solve the system of equations using the elimination method, we can start with the following equations:
- \( 6c - 9d = 111 \) (Equation 1)
- \( 5c - 9d = 103 \) (Equation 2)
We can eliminate \(d\) by subtracting Equation 2 from Equation 1:
\[ (6c - 9d) - (5c - 9d) = 111 - 103 \]
This simplifies to:
\[ 6c - 9d - 5c + 9d = 8 \]
Which further simplifies to:
\[ c = 8 \]
Now that we have the value of \(c\), we can substitute it back into one of the original equations to find \(d\). Let's use Equation 2:
\[ 5c - 9d = 103 \]
Substituting \(c = 8\):
\[ 5(8) - 9d = 103 \] \[ 40 - 9d = 103 \] \[ -9d = 103 - 40 \] \[ -9d = 63 \] \[ d = -\frac{63}{9} \] \[ d = -7 \]
Thus, we have \(c = 8\) and \(d = -7\).
The solution in ordered pair form is:
\[ \boxed{(8, -7)} \]