Answer:
The solution of the system is: [tex]x=2, y=5[/tex]
Step-by-step explanation:
The given system of equations is.......
[tex]-x-3y=-17\\ \\ 2x-6y=-26[/tex]
So, the augmented matrix will be: [tex]\left[\begin{array}{cccc}-1&-3&|&-17\\2&-6&|&-26\\\end{array}\right][/tex]
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..........
[tex]\left[\begin{array}{cccc}1&3&|&17\\2&-6&|&-26\\\end{array}\right][/tex]
Row operation 2: Add -2 times the 1st row to the 2nd row. So.......
[tex]\left[\begin{array}{cccc}1&3&|&17\\0&-12&|&-60\\\end{array}\right][/tex]
Row operation 3: Multiply the 2nd row by [tex]-\frac{1}{12}[/tex]. So.......
[tex]\left[\begin{array}{cccc}1&3&|&17\\0&1&|&5\\\end{array}\right][/tex]
Row operation 4: Add -3 times the 2nd row to the 1st row. So........
[tex]\left[\begin{array}{cccc}1&0&|&2\\0&1&|&5\\\end{array}\right][/tex]
Now, from this reduced row echelon form of the augmented matrix, we can get that [tex]x=2[/tex] and [tex]y=5[/tex]
So, the solution of the system is: [tex]x=2, y=5[/tex]
