Contradictory equations Question: Find whether the solution set of $$\begin{cases}2x = 1\\ y + 5 = x\\ x = y + 3\end{cases}$$ is a singleton.
My attempt: Rewriting the first equation will give us $x = \frac{1}{2}$.
The other two equations can be written as $x - y = 5$ and $x - y = 3$.
Now, the solution of these equations is $\emptyset$. 
So we can say that the solution set of $$\begin{cases}2x = 1\\ y + 5 = x\\ x = y + 3\end{cases}$$ is not singleton.
Kindly verify and throw some insights.

A vertical line ( first equation ) cuts two parallel lines ( last two ) transversely, creating two points of intersection or two solutions. 
If there were three (non-concurrent) lines then there would be three points of intersection enclosing a triangle.
