To solve the system of equations:
- \( 6c - 9d = 11 \) (Equation 1)
- \( 5c - 9d = 103 \) (Equation 2)
We can start by eliminating \( d \) from the equations. Since both equations have \(-9d\) as a term, we can subtract Equation 1 from Equation 2.
Subtract Equation 1 from Equation 2:
\[ (5c - 9d) - (6c - 9d) = 103 - 11 \]
This simplifies to:
\[ 5c - 6c + 9d - 9d = 92 \] \[ -c = 92 \]
Thus, we find:
\[ c = -92 \]
Now that we have \( c \), we can substitute \( c = -92 \) back into one of the original equations to find \( d \). We'll use Equation 1:
\[ 6(-92) - 9d = 11 \]
Calculating \( 6(-92) \):
\[ -552 - 9d = 11 \]
Now, isolate \( d \):
\[ -9d = 11 + 552 \] \[ -9d = 563 \]
Dividing both sides by -9 gives:
\[ d = -\frac{563}{9} \]
Now we have \( c \) and \( d \):
\[ c = -92, \quad d = -\frac{563}{9} \]
Thus, the solution to the system of equations in simplified ordered pair form is:
\[ \boxed{\left( -92, -\frac{563}{9} \right)} \]
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