Question 145808

Start with the given system of equations:


{{{3x-y=6}}}

{{{3x+4y=-9}}}





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=6}}} Start with the given equation



{{{-y=6-3x}}}  Subtract {{{3 x}}} from both sides



{{{-y=-3x+6}}} Rearrange the equation



{{{y=(-3x+6)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-3/-1)x+(6)/(-1)}}} Break up the fraction



{{{y=3x-6}}} Reduce



Now lets graph {{{y=3x-6}}} (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-6) }}} Graph of {{{y=3x-6}}}




So let's solve for y on the second equation


{{{3x+4y=-9}}} Start with the given equation



{{{4y=-9-3x}}}  Subtract {{{3 x}}} from both sides



{{{4y=-3x-9}}} Rearrange the equation



{{{y=(-3x-9)/(4)}}} Divide both sides by {{{4}}}



{{{y=(-3/4)x+(-9)/(4)}}} Break up the fraction



{{{y=(-3/4)x-9/4}}} Reduce




Now lets add the graph of {{{y=(-3/4)x-9/4}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, 3x-6,(-3/4)x-9/4) }}} Graph of {{{y=3x-6}}}(red) and {{{y=(-3/4)x-9/4}}}(green)


From the graph, we can see that the two lines intersect at the point (1,-3) 



So the system is consistent and independent