The first four correspond to the variables x, y, z and u and the fifth column corresponds to the right-sides.
The thing i'm asking is, how many solutions does this system of questions have and how do you find that out? Not sure how to think of it because there's no "Free variable"
Write down the equations and you get: $$ x+\frac{88}{87}u=\frac5{29}\\ y+\frac{317}{87}u=\frac{77}{29}\\ z-\frac{184}{87}u=-\frac{21}{29} $$ You see that you can easily get a solution depending on $u$ and $u$ is a free variable: $$ x=\frac5{29}-\frac{88}{87}u\\ y=\frac{77}{29}-\frac{317}{87}u\\ z=-\frac{21}{29}+\frac{184}{87}u $$