Question 123343



Start with the given system of equations:


{{{2x-y=4}}}

{{{2x-y=6}}}





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


{{{2x-y=4}}} Start with the given equation



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



{{{-y=-2x+4}}} Rearrange the equation



{{{y=(-2x+4)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-2/-1)x+(4)/(-1)}}} Break up the fraction



{{{y=2x-4}}} Reduce



Now lets graph {{{y=2x-4}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)



{{{ graph( 600, 600, -10, 10, -10, 10, 2x-4) }}} Graph of {{{y=2x-4}}}




So let's solve for y on the second equation


{{{2x-y=6}}} Start with the given equation



{{{-y=6-2x}}}  Subtract {{{2 x}}} from both sides



{{{-y=-2x+6}}} Rearrange the equation



{{{y=(-2x+6)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-2/-1)x+(6)/(-1)}}} Break up the fraction



{{{y=2x-6}}} Reduce




Now lets add the graph of {{{y=2x-6}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, 2x-4,2x-6) }}} Graph of {{{y=2x-4}}}(red) and {{{y=2x-6}}}(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.