Question

What is the solution to this system of equation in simplified ordered pair form using elimination?
6c-9d=111
5c-9d=103

Answer 1

To solve the system of equations using the elimination method, we can start with the following equations:

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

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