the augmented matrix is filling in the numbers corresponding to the given letters in the equations
the first equation is x-y +8z = 7
so the first row in the matrix would be 1 ( there is 1x) -1 ( there is 1 negative y) 8 ( there are 8 z's) and then the answer is 7
then follow this step for the other 2 equations
see attached picture for answer: