Find positive integers that satisfy

Question

Find positive integers that satisfy

Answer 1

Looks like z will be the free variable since there are only the 2 equations.

[1 1 1 6]

[1 6 7 34]

r2 = r2-r1

[1 1 1 6]

[0 5 6 28]

r2 = r2/5

[1 1 1 6]

[0 1 6/5 28/5]

From the last row

y = (28-6z)/5

let z = 3

y = (28-18)/5 = 2

From the first equation

x + 2 + 3 = 6 --> x = 1

x=1, y=2, z=3