Answer:
The correct option is C) (4,4)
Step-by-step explanation:
Given linear system is :
\(-x+6y=20\)
\(-x+3y=8\)
Solve using Gauss - jordan elimination
It is an algorithm that can be used to solve systems of linear equations and to find the inverse of any invertible matrix.
\(\:\begin{pmatrix}-1&6&20\\ \:-1&3&8\end{pmatrix}\)
\(\mathrm{Reduce\:matrix\:to\:row\:echelon\:form}\:\begin{pmatrix}a&\cdots &b\\ 0&\ddots &\vdots \\ 0&0&c\end{pmatrix}\)
Divide row(1) by -1
\(\begin{pmatrix}1&-6&-20\\ \:-1&3&8\end{pmatrix}\)
Add row(1) to row(2)
\(\begin{pmatrix}1&-6&-20\\ \:0&-3&-12\end{pmatrix}\)
Divide row(2) by -3
\(\begin{pmatrix}1&-6&-20\\ \:0&1&4\end{pmatrix}\)
Add (6 * row(2) ) to row(1)
\(=\begin{pmatrix}1&0&4\\ 0&1&4\end{pmatrix}\)
Hence the corresponding values of x and y are (4, 4)
Therefore, the correct option is C) (4,4)
