Question 144155



Start with the given system of equations:


{{{5x-y=25}}}

{{{5x+6y=-10}}}





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


{{{5x-y=25}}} Start with the given equation



{{{-y=25-5x}}}  Subtract {{{5 x}}} from both sides



{{{-y=-5x+25}}} Rearrange the equation



{{{y=(-5x+25)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-5/-1)x+(25)/(-1)}}} Break up the fraction



{{{y=5x-25}}} Reduce



Now lets graph {{{y=5x-25}}} (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, 5x-25) }}} Graph of {{{y=5x-25}}}




So let's solve for y on the second equation


{{{5x+6y=-10}}} Start with the given equation



{{{6y=-10-5x}}}  Subtract {{{5 x}}} from both sides



{{{6y=-5x-10}}} Rearrange the equation



{{{y=(-5x-10)/(6)}}} Divide both sides by {{{6}}}



{{{y=(-5/6)x+(-10)/(6)}}} Break up the fraction



{{{y=(-5/6)x-5/3}}} Reduce




Now lets add the graph of {{{y=(-5/6)x-5/3}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, 5x-25,(-5/6)x-5/3) }}} Graph of {{{y=5x-25}}}(red) and {{{y=(-5/6)x-5/3}}}(green)


From the graph, we can see that the two lines intersect at the point (4,-5). Since the two graphs intersect each other at one point, this means that the system is consistent and independent.