ANSWER
[tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]
EXPLANATION
Given;
[tex]4x-12y=1[/tex]
and
[tex]6x+4y=4[/tex]
The augmented matrix of the two linear equation is given by;
[tex]\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right][/tex]
We now perform row operations;
[tex]\frac{1}{4}\times R_1 \rightarrow R_1 [/tex].
This gives us
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right][/tex]
[tex]R_2-6R_1 \rightarrow R_2[/tex]
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right][/tex]
[tex]\frac{1}{22}R _2 \rightarrow R_2[/tex]
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]
[tex]R_1+3R_2 \rightarrow R_1[/tex]
[tex]\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]
Hence [tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]
