Question

What is the solution to this system of equation in simplified ordered pair form?
6c-9d=11
5c-9d=103

Answer 1

To solve the system of equations:

1. \( 6c - 9d = 11 \) (Equation 1)
2. \( 5c - 9d = 103 \) (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:

\[
\boxed{\left( -92, -\frac{563}{9} \right)}
\]