Question 145825
Notice how the first equation is already in y form


So lets graph {{{y=-x-9}}} (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, -x-9) }}} Graph of {{{y=-x-9}}}




So let's solve for y on the second equation


{{{5x-4y=-27}}} Start with the given equation



{{{-4y=-27-5x}}}  Subtract {{{5 x}}} from both sides



{{{-4y=-5x-27}}} Rearrange the equation



{{{y=(-5x-27)/(-4)}}} Divide both sides by {{{-4}}}



{{{y=(-5/-4)x+(-27)/(-4)}}} Break up the fraction



{{{y=(5/4)x+27/4}}} Reduce




Now lets add the graph of {{{y=(5/4)x+27/4}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -x-9,(5/4)x+27/4) }}} Graph of {{{y=-x-9}}}(red) and {{{y=(5/4)x+27/4}}}(green)


From the graph, we can see that the two lines intersect at the point (-7,-2) 


So this means that the system is consistent and independent.