Question 145828
note: I'm replacing "u" with "x" and "v" with "y" so I can graph the equations.



Start with the given system of equations:


{{{3x+y=16}}}

{{{3x=y+26}}}





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=16}}} Start with the given equation



{{{y=16-3x}}}  Subtract {{{3 x}}} from both sides



{{{y=-3x+16}}} Rearrange the equation





Now lets graph {{{y=-3x+16}}} (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+16) }}} Graph of {{{y=-3x+16}}}




So let's solve for y on the second equation


{{{3x=y+26}}} Start with the given equation



{{{3x-26=y}}}  Subtract {{{26}}} from both sides



{{{y=3x-26}}} Rearrange the equation




Now lets add the graph of {{{y=3x-26}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -3x+16,3x-26) }}} Graph of {{{y=-3x+16}}}(red) and {{{y=3x-26}}}(green)


From the graph, we can see that the two lines intersect at the point (7,-5) 



So this means that the system is consistent and independent.