Question 170731


Start with the given system of equations:



{{{system(10x-4y=3,5x-2y=6)}}}



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



Let's graph the first equation:



{{{10x-4y=3}}} Start with the first equation.



{{{-4y=3-10x}}} Subtract {{{10x}}} from both sides.



{{{y=(3-10x)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=(5/2)x-3/4}}} 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,(5/2)x-3/4)
)}}} Graph of {{{y=(5/2)x-3/4}}}.



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Now let's graph the second equation:



{{{5x-2y=6}}} Start with the second equation.



{{{-2y=6-5x}}} Subtract {{{5x}}} from both sides.



{{{y=(6-5x)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{y}}}.



{{{y=(5/2)x-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,(5/2)x-3)
)}}} Graph of {{{y=(5/2)x-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,(5/2)x-3/4,(5/2)x-3)
)}}} Graph of {{{y=(5/2)x-3/4}}} (red). Graph of {{{y=(5/2)x-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.