I am working the next set of lineal equations
$\begin{cases}
7x+2y=1 & 1\\
21x+6y=3 & 2
\end{cases}$
So multiplying (1) by -3
$7x+2y=1(-3)$
$-21x-6y=-3$
Adding both equations
$21x+6y=3$
$-21x-6y=-3$
0x+0y=0
0=0
This seems to be a uncompatible/no solutions system, but graphically the system is
So there is a common point in (0,1/2),then it would have ,at least, one solution.
And this solution solve the equations:
$\begin{cases}
7(0)+2\frac{1}{2}=1 & \\
21(0)+6\frac{1}{2}=3 &
\end{cases}$
but I have tested the system using the usual methods and gives the $\emptyset$.
Then this system has solution or not?
UPDATE
The graphs are wrong the right one is
so it has infinite solutions.