-2x + 2y = 1

Consider the system of given equations

x - y = 6

-2x + 2y = 1

Now put y = 0, 1, 2 in x - y = 6 (isolate x) we get

Consider the second equation and isolate y again

-2x + 2y = 1

$\Rightarrow$ y =

$\frac{1}{2}$ + x

Now put x = 0, 1, 2 in -2x + 2y = 1

Graph the above points

From
the graph it appears that the two lines are parallel. As the lines are
parallel they have different intercepts and will not intersect. So there
will be no solution to the given system of equations.