Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2007 / Paper 2 / Section B / 7 / d

Subtracting the first and third equations gives $\mu (x-z)=0$. Since $\mu \ne 0$, $x=z$, and the second equation gives $x=z=1$. The first then gives $y=1-\mu$, so the unique solution of the system of linear equations is

At $\mu =0$, the first and third equations both reduce to $y=1$, while the second gives $x+z=2$. All solutions form the straight lineThe limit of the nonzero-$\mu$ solution selects only the point $(1,1,1)$ on this whole line; setting a parameter to its singular value can enlarge the solution set.