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

Answer:

$x=-2,y=3$

Step-by-step explanation:

The given system of equations is

$2x+4y=8$

and

$6x+3y=-3$

The augmented matrix is

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

$\frac{1}{2}R_1\to R_1$

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

$-6R_1+R_2\to R_2$

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

$-\frac{1}{9}R_2\to R_2$

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

$-2R_2+R_1\to R_1$

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

Hence $x=-2,y=3$