Question

Please help!! Solve the system using an augmented matrix. Show all work

Answer 1

Answer:

The solution of the system is:  $x=2, y=5$

Step-by-step explanation:

The given system of equations is.......

$-x-3y=-17\\ \\ 2x-6y=-26$

So, the augmented matrix will be:   $\left[\begin{array}{cccc}-1&-3&|&-17\\2&-6&|&-26\\\end{array}\right]$

Now, we will transform the augmented matrix to the reduced row echelon form using row operations.

Row operation 1 :  Multiply the 1st row by -1. So..........

$\left[\begin{array}{cccc}1&3&|&17\\2&-6&|&-26\\\end{array}\right]$

Row operation 2:  Add -2 times the 1st row to the 2nd row. So.......

$\left[\begin{array}{cccc}1&3&|&17\\0&-12&|&-60\\\end{array}\right]$

Row operation 3:  Multiply the 2nd row by $-\frac{1}{12}$. So.......

$\left[\begin{array}{cccc}1&3&|&17\\0&1&|&5\\\end{array}\right]$

Row operation 4:  Add -3 times the 2nd row to the 1st row. So........

$\left[\begin{array}{cccc}1&0&|&2\\0&1&|&5\\\end{array}\right]$

Now, from this reduced row echelon form of the augmented matrix, we can get that $x=2$ and $y=5$

So, the solution of the system is:  $x=2, y=5$