Question

Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system.
2x + 9y = 4
3x + 7y = -7

Answer 1

\[\left[\begin{matrix}2 & 9 & 4\\ 3 & 7 & -7\end{matrix}\right]\]
switch row 1 and row 2, and subtract the new row 2 from the new row 1
\[\left[\begin{matrix}1 & -2 & -11\\ 2 & 9 & 4\end{matrix}\right]\]
subtract twice row 1 from row 2
\[\left[\begin{matrix}1 & -2 & -11\\ 0 & 13 & 26\end{matrix}\right]\]
divide row 2 by 13
\[\left[\begin{matrix}1 & -2 & -11\\ 0 & 1 & 2\end{matrix}\right]\]
add 2 times row 2 to row 1
\[\left[\begin{matrix}1 & 0 & -7\\ 0 & 1 & 2\end{matrix}\right]\]
done!

That's gauss-jordan elimination.