What is the solution to this system of equation in simplified ordered pair form?

6c-9d=111
5c-9d=103

1 answer

To solve the system of equations:

  1. \(6c - 9d = 111\) (Equation 1)
  2. \(5c - 9d = 103\) (Equation 2)

We can eliminate \(d\) by subtracting Equation 2 from Equation 1.

Subtract Equation 2 from Equation 1:

\[ (6c - 9d) - (5c - 9d) = 111 - 103 \]

This simplifies to:

\[ 6c - 5c - 9d + 9d = 111 - 103 \]

\[ c = 8 \]

Now that we have \(c = 8\), we can substitute this value into either of the original equations to find \(d\). Using Equation 2:

\[ 5c - 9d = 103 \]

Substituting \(c = 8\):

\[ 5(8) - 9d = 103 \]

\[ 40 - 9d = 103 \]

Now isolate \(d\):

\[ -9d = 103 - 40 \]

\[ -9d = 63 \]

\[ d = \frac{63}{-9} = -7 \]

Thus, the solution to the system of equations in ordered pair form is:

\[ \boxed{(8, -7)} \]