Question

Solve each system using a matrix

Answer 1

ANSWER

$x=\frac{1}{2}$ and $y=\frac{1}{4}$

EXPLANATION

Given;

$4x-12y=1$

and

$6x+4y=4$

The augmented matrix of the two linear equation is given by;

$\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right]$

We now perform row operations;

$\frac{1}{4}\times R_1 \rightarrow R_1$.

This gives us

$\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right]$

$R_2-6R_1 \rightarrow R_2$

$\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right]$

$\frac{1}{22}R _2 \rightarrow R_2$

$\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right]$

$R_1+3R_2 \rightarrow R_1$

$\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right]$

Hence $x=\frac{1}{2}$ and $y=\frac{1}{4}$