The number of solutions to a system of linear equations Can anyone suggest a formal proof that a system of linear equations can have no solution, one solution or infinitely many solutions? 

What you are asking for is an example. In $\mathbb{R}^1$, consider


*

*$0\cdot x=1$;

*$x=2016$;

*$x=x$.


In $\mathbb{R}^2$, consider  


*

*$0\cdot x+0\cdot y=1$;  

*$$\begin{cases}
x=2016\\
y=2016
\end{cases}
$$  

*$x=y$;  


Can you see that how this example could be generalized to $\mathbb{R}^n$?
