document.write( "Question 473087: Determine if the system is Dependent, Inconsistent or has a Unique Solution. If it has a solution, find the solution for x and y using any method.
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\n" ); document.write( "12x – 3y = 21
\n" ); document.write( "4x – y = 9 \n" ); document.write( "
Algebra.Com's Answer #324435 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Solve the System of Equations by Graphing

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\n" ); document.write( " Start with the given system of equations:
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\n" ); document.write( " \"12x-3y=21\"
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\n" ); document.write( " \"4x-y=9\"
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\n" ); document.write( " In order to graph these equations, we need to solve for y for each equation.
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\n" ); document.write( " So let's solve for y on the first equation
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\n" ); document.write( " \"12x-3y=21\" Start with the given equation
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\n" ); document.write( " \"-3y=21-12x\" Subtract \"12+x\" from both sides
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\n" ); document.write( " \"-3y=-12x%2B21\" Rearrange the equation
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\n" ); document.write( " \"y=%28-12x%2B21%29%2F%28-3%29\" Divide both sides by \"-3\"
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\n" ); document.write( " \"y=%28-12%2F-3%29x%2B%2821%29%2F%28-3%29\" Break up the fraction
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\n" ); document.write( " \"y=4x-7\" Reduce
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\n" ); document.write( " Now lets graph \"y=4x-7\" (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x-7%29+\" Graph of \"y=4x-7\"
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " \"4x-y=9\" Start with the given equation
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\n" ); document.write( " \"-y=9-4x\" Subtract \"4+x\" from both sides
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\n" ); document.write( " \"-y=-4x%2B9\" Rearrange the equation
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\n" ); document.write( " \"y=%28-4x%2B9%29%2F%28-1%29\" Divide both sides by \"-1\"
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\n" ); document.write( " \"y=%28-4%2F-1%29x%2B%289%29%2F%28-1%29\" Break up the fraction
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\n" ); document.write( " \"y=4x-9\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=4x-9\" to our first plot to get:
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x-7%2C4x-9%29+\" Graph of \"y=4x-7\"(red) and \"y=4x-9\"(green)
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\n" ); document.write( " From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.
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