You can put this solution on YOUR website! There are many ways to use matrices to solve systems of equations like this. I'll use the one that is often the first one taught:
Add -2*Row 1 to the second row and 2*row 1 to the third row:
Add -3*Row 2 to the first row and -5*Row 2 to the third row:
Multiply Row 3 by -1/31:
Add 19*Row 3 to row 1 and add -5*Row 3 to the second row:
Solution: (1, 0, -3)