Whatever I do, I can't grasp it. The letters confuses me, as I don't know exactly what I need to do.
For example, I get z = 14 / 15 y, but what's next? Should I plug the whole y function once again in z?
Could someone give me a step by step solution for this one? I want to understand it, yet I can't grasp it somehow. Have an exam tomorrow andddd this is driving me nuts.
All your equations are homogeneous. Any solution can be multiplied by any constant and get another solution. You can choose any variable to be any value you want and derive the other two. As you have correctly found $z=\frac {14}{15}y$ and the first equation says $x=\frac 15y$ we can choose $y=1$ and get a solution $$x=\frac 15\\y=1\\z=\frac {14}{15}$$ Any multiple of this is also a solution. The information of interest is that $y$ is the highest with $z$ close behind.