document.write( "Question 759929: Determine whether the pair of lines is parallel, perpendicular, or neither 2x+y=5 , 6×+3y=4 \n" ); document.write( "
Algebra.Com's Answer #462296 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"+6x%2B3y=4\"\r
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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( " \"2x%2By=5\"
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\n" ); document.write( " \"6x%2B3y=4\"
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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( " \"2x%2By=5\" Start with the given equation
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\n" ); document.write( " \"1y=5-2x\" Subtract \"2+x\" from both sides
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\n" ); document.write( " \"1y=-2x%2B5\" Rearrange the equation
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\n" ); document.write( " \"y=%28-2x%2B5%29%2F%281%29\" Divide both sides by \"1\"
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\n" ); document.write( " \"y=%28-2%2F1%29x%2B%285%29%2F%281%29\" Break up the fraction
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\n" ); document.write( " \"y=-2x%2B5\" Reduce
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\n" ); document.write( " Now lets graph \"y=-2x%2B5\" (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+-2x%2B5%29+\" Graph of \"y=-2x%2B5\"
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " \"6x%2B3y=4\" Start with the given equation
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\n" ); document.write( " \"3y=4-6x\" Subtract \"6+x\" from both sides
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\n" ); document.write( " \"3y=-6x%2B4\" Rearrange the equation
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\n" ); document.write( " \"y=%28-6x%2B4%29%2F%283%29\" Divide both sides by \"3\"
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\n" ); document.write( " \"y=%28-6%2F3%29x%2B%284%29%2F%283%29\" Break up the fraction
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\n" ); document.write( " \"y=-2x%2B4%2F3\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=-2x%2B4%2F3\" 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+-2x%2B5%2C-2x%2B4%2F3%29+\" Graph of \"y=-2x%2B5\"(red) and \"y=-2x%2B4%2F3\"(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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