Question

By using the method of matrices, solve the following the simultaneous equation.
2x - y =4
3x - y = 5
Could someone explain in detail with the working steps?

Answer 1

there are a few ways to do this with matrix manipulations.

the idea tho is to establish rules used from elimination method:

you can multiply rows, and add columns

Answer 2

\begin{matrix}
*1/2)&2&-1&|&4\\
&3&-1&|&5\\
\end{matrix}


\begin{matrix}
*-3)&1&-1/2&|&2\\
&3&-1&|&5\\
\end{matrix}

\begin{matrix}
&-3&3/2&|&-6\\
+)&3&-1&|&5\\
&-&-&-&-\\
&0&1/2&|&-1
\end{matrix}

now we can reconstruct it back subbing in this new row[2]

\begin{matrix}
&1&-1/2&|&2\\
&0&1/2&|&-1
\end{matrix}

another addition of columns and will get rid of the 1/2 parts and so on and so forth

Answer 3

the easier matrix move to do is to use cramers rule:
\begin{matrix}
x&y&|&=\\
-&-&-&-\\
a&b&|&n\\
c&d&|&m
\end{matrix}
\[y=\frac{am-cn}{ad-cb}\]
\[x=\frac{bm-dn}{cb-ad}\]