Question

Solve each system using a matrix

4x-12y=-1
6x+4y=4





1 1 | 4
-2 -5 -11

Answer 1

`x=(1)/(2)` and
`y=(1)/(4)`

Step-by-step 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;

`(1)/(4)* R_1 \rightarrow R_1`.

This gives us

`\left[\begin{array}{ccc}1&-3|&(-1)/(4)\\6\:&\:\:\:4|&4\end{array}\right]`

`R_2-6R_1 \rightarrow R_2`

`\left[\begin{array}{ccc}1&-3|&(-1)/(4)\\0\:&\:\:\:22|&(11)/(2)\end{array}\right]`

`(1)/(22)R _2 \rightarrow R_2`

`\left[\begin{array}{ccc}1&-3|&(-1)/(4)\\0\:&\:\:\:1|&(1)/(4)\end{array}\right]`

`R_1+3R_2 \rightarrow R_1`

`\left[\begin{array}{ccc}1&0|&(1)/(2)\\0\:&\:\:\:1|&(1)/(4)\end{array}\right]`

Hence
`x=(1)/(2)` and
`y=(1)/(4)`