Question 743434
{{{3x-5y=1}}}
{{{6x-10y=4}}}


First we solve for x in the first equation
{{{3x=1+5x}}}

{{{x=(1+5y)/3}}}

The second equation,
{{{6x-10y=4}}}
becomes...

{{{6((1+5y)/3)-10y=4}}}
which we simplify as follows...

{{{2(1+5y)-10y=4}}}
{{{2+10y-10y=4}}}
{{{2=4}}}

this clearly a contradiction. This contradiction tells us that our system has no solution. (Whenever we arrive at a contradiction after following the solution method correctly we know that the system has no solution. If we arrive at an identity we know that the lines are coincident)