Question 29924
both of these are already in Ax+By=C form as opposed to y=mx+b

1X + 3y = 7
4X +12y =-9

if we multiply the top equation by -4 we get ...
-4x - 12y = -28
 4x + 12y =  -9  now we add tthe two equations
 0x +  0y = -37
 0 = -37 NO! this is a false statement.  Lets see if we did it right.
lets look at the lines once more and this time solve each in y=mx+b format
{{{ 1X + 3y = 7}}} and {{{ 4X +12y =-9 }}}
{{{ 3y=-1x+7 }}} and {{{ 12y=-4x-9 }}}
{{{ y=-1x/3 + 7/3 }}} and {{{ y=-4x/12 - 9/12 }}} reduce the fractions in the second equation
{{{ y=-1x/3 - 3/4 }}} In this form {{{ y=mx+b }}} BOTH equations have m = -1/3

That means that these two lines are parallel and NEVER cross, therefore there is no Solution so :
{{{ 0 <> -37 }}} was done correctly, but there is NO SOLUTION.