Question

Use the matrix method to solve the system of equations 2 x + 4 y = 8 and 6 x + 3 y = -3. The resulting matrix is:



Answer 1

`x=-2,y=3`

Explanation:

The given system of equations is

`2x+4y=8`

and

`6x+3y=-3`

The augmented matrix is

`\left[\begin{array}{ccc}2&4&|8\\6&3&|-3\end{array}\right]`

`(1)/(2)R_1\to R_1`

`\left[\begin{array}{ccc}1&2&|4\\6&3&|-3\end{array}\right]`

`-6R_1+R_2\to R_2`

`\left[\begin{array}{ccc}1&2&|4\\0&-9&|-27\end{array}\right]`

`-(1)/(9)R_2\to R_2`

`\left[\begin{array}{ccc}1&2&|4\\0&1&|3\end{array}\right]`

`-2R_2+R_1\to R_1`

`\left[\begin{array}{ccc}1&0&|-2\\0&1&|3\end{array}\right]`

Hence
`x=-2,y=3`