Question 463770
Proceed with Gauss-Jordan reduction:

{{{(matrix(3,4,3, 1,-2, 10,0,  2,  -3,  4,0 ,  0,   1,  4))}}}

~{{{(matrix(3,4,3, 1,-2, 10,0,  2,  0, 16,0 ,  0,   1,  4))}}}, by 3R3 + R2

~{{{(matrix(3,4,3, 1,0, 18,0,  2,  0, 16,0 ,  0,   1,  4))}}}, by 2R3 + R1

~{{{(matrix(3,4,3, 1,0, 18,0,  1,  0, 8,0 ,  0,   1,  4))}}}, R2/2

~{{{(matrix(3,4,3, 0,0, 10,0,  1,  0, 8,0 ,  0,   1,  4))}}}, by -R2 + R1

~{{{(matrix(3,4,1, 0,0, 10/3,0,  1,  0, 8,0 ,  0,   1,  4))}}}, by R1/3

Therefore, x = 10/3, y = 8, and z = 4.