Question 458297
I will just do #2.

{{{(matrix(3,4,1,2,-3,-5,1,4,-7,-13,1,-1,2,1))}}}
~ {{{(matrix(3,4,1,2,-3,-5,0,1,-2,-4,0,1,-5/3,-2))}}}, after doing -R1 + R2 and -R1 + R3

~{{{(matrix(3,4,1,2,-3,-5,0,1,-2,-4,0,0,1/3,2))}}}, after doing -R2 + R3
~{{{(matrix(3,4,1,2,-3,-5,0,1,-2,-4,0,0,1,6))}}}, after 3R3.

~{{{(matrix(3,4,1,2,-3,-5,0,1,0,8,0,0,1,6))}}}after 2R3 + R2

~{{{(matrix(3,4,1,0,0,-3,0,1,0,8,0,0,1,6))}}}, after 3R3 + R1 and -2R2 + R1
Hence x = -3, y = 8, and z = 6.