Question

use elimination to solve the system of equations.
6c - 9d = 111
5c - 9d = 103
( , )

Explanation:

Step1: Subtract the two equations

Subtract the second equation from the first to eliminate \(d\).
\((6c - 9d)-(5c - 9d)=111 - 103\)
Simplify the left side: \(6c - 9d - 5c + 9d=c\)
Simplify the right side: \(111 - 103 = 8\)
So, \(c = 8\).

Step2: Substitute \(c = 8\) into one equation

Substitute \(c = 8\) into the second equation \(5c-9d = 103\).
\(5\times8-9d=103\)
Calculate \(5\times8 = 40\), so \(40-9d = 103\).

Step3: Solve for \(d\)

Subtract 40 from both sides: \(-9d=103 - 40\)
\(103 - 40 = 63\), so \(-9d = 63\).
Divide both sides by \(-9\): \(d=\frac{63}{-9}=-7\).

Answer:

\((8, -7)\)