Question 126086


Start with the given system of equations:


{{{6x-2y=4}}}

{{{12x-6y=8}}}





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


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



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



{{{-2y=-6x+4}}} Rearrange the equation



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



{{{y=(-6/-2)x+(4)/(-2)}}} Break up the fraction



{{{y=3x-2}}} Reduce



Now lets graph {{{y=3x-2}}} (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-2) }}} Graph of {{{y=3x-2}}}




So let's solve for y on the second equation


{{{12x-6y=8}}} Start with the given equation



{{{-6y=8-12x}}}  Subtract {{{12 x}}} from both sides



{{{-6y=-12x+8}}} Rearrange the equation



{{{y=(-12x+8)/(-6)}}} Divide both sides by {{{-6}}}



{{{y=(-12/-6)x+(8)/(-6)}}} Break up the fraction



{{{y=2x-4/3}}} Reduce




Now lets add the graph of {{{y=2x-4/3}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, 3x-2,2x-4/3) }}} Graph of {{{y=3x-2}}}(red) and {{{y=2x-4/3}}}(green)


From the graph, we can see that there is one solution (since one intersection corresponds to one solution)



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Answer:



So the system has one solution