Question 206974


Start with the given system of equations:



{{{system(3x-9y=81,2x-6y=-4)}}}



In order to graph these equations, we <font size="4"><b>must</b></font> solve for y first.



Let's graph the first equation:



{{{3x-9y=81}}} Start with the first equation.



{{{-9y=81-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(81-3x)/(-9)}}} Divide both sides by {{{-9}}} to isolate {{{y}}}.



{{{y=(1/3)x-9}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,(1/3)x-9)
)}}} Graph of {{{y=(1/3)x-9}}}.



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Now let's graph the second equation:



{{{2x-6y=-4}}} Start with the second equation.



{{{-6y=-4-2x}}} Subtract {{{2x}}} from both sides.



{{{y=(-4-2x)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{y}}}.



{{{y=(1/3)x+2/3}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,(1/3)x+2/3)
)}}} Graph of {{{y=(1/3)x+2/3}}}.



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Now let's graph the two equations together:



{{{drawing(500,500,-10,10,-10,10,
grid(1),
graph(500,500,-10,10,-10,10,(1/3)x-9,(1/3)x+2/3)
)}}} Graph of {{{y=(1/3)x-9}}} (red). Graph of {{{y=(1/3)x+2/3}}} (green)



From the graph, we can see that the two lines are parallel, which means that they will <font size="4"><b>never</b></font> intersect. 



So there are no solutions. This means that the system of equations is inconsistent.