Question 103928
Let's say you have the two equations: {{{y=2x+1}}} and {{{y=2x-4}}}


{{{2x+1=2x-4}}} Set the two equations equal to one another



{{{2x+1-2x=-4}}} Subtract 2x from both sides



{{{2x-2x=-4-1}}} Subtract 1 from both sides



{{{0x=-5}}} Subtract 



{{{0=-5}}} Simplify



Notice we have a contradiction (0 will never be equal to -5). Since this statement is never true, there are no solutions.



Notice if we graph the two equations, we get:



{{{ graph( 500, 500, -6, 5, -10, 10,2x+1,2x-4) }}} Graph of {{{y=2x+1}}} (red) and {{{y=2x-4}}} (green)



Notice the two lines are parallel and will never intersect. So this means the system has no solutions.