Write solution to system if it exists

Question

[1 0 5 | -5

 0 1 -3|4

 0 0 0 | 0 ]

 

I got infinite solutions but wanted to be sure!!

Answer 1

x+5z = -5

y-3z = 4

0x+0y+0z = 0

there's really just 2 equations for 3 unknowns which means an infinite number of solutions

for example

y=4, z=0, x=-5

or

y=0, z=-4/3, x =-5-5(-4/3) = -5+20/3 = 5/3

or endless more solutions