Question 145809
note: I'm replacing "u" with "x" and "v" with "y"


Start with the given system of equations:


{{{3x+y=15}}}

{{{3x+y=33}}}





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


{{{3x+y=15}}} Start with the given equation



{{{y=15-3x}}}  Subtract {{{3 x}}} from both sides



{{{y=-3x+15}}} Rearrange the equation



Now lets graph {{{y=-3x+15}}} (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, -3x+15) }}} Graph of {{{y=-3x+15}}}




So let's solve for y on the second equation


{{{3x+y=33}}} Start with the given equation



{{{y=33-3x}}}  Subtract {{{3 x}}} from both sides



{{{y=-3x+33}}} Rearrange the equation





Now lets add the graph of {{{y=-3x+33}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -3x+15,-3x+33) }}} Graph of {{{y=-3x+15}}}(red) and {{{y=-3x+33}}}(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.