In first equation, x has coefficient 1 and y has coefficient 4 and is equal to 8
In first equation, x has coefficient 2 and y has coefficient 1 and is equal to 9
So augmented matrix would looks like this:
[tex]\left[\begin{array}{cc|c}1&4&8\\2&1&9\end{array}\right][/tex]
Your goal is to transform matrix to look like this:
[tex] \left[\begin{array}{cc|c}1&0&x_{\text{answer}}\\0&1&y_{\text{answer}}\end{array}\right][/tex]
Steps to reach there:
Subtract first row from second row two times:
[tex]\left[\begin{array}{cc|c}1&4&8\\0&-7&-7\end{array}\right][/tex]
Multiple second row by -1/7:
[tex]\left[\begin{array}{cc|c}1&4&8\\0&1&1\end{array}\right][/tex]
Now subtract second row from first row 4 times:
[tex]\boxed{\left[\begin{array}{cc|c}1&0&4\\0&1&1\end{array}\right]}[/tex]
Which translate to
[tex]x+0y = 4\\\ \\0x+y=1[/tex]
So then x = 4 and y = 1.
Hope this helps.
