document.write( "Question 1128374: Solving a System of Equations. Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in ordered-pair form.\r
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\n" ); document.write( "-1/4x-3/2y=1 \n" ); document.write( "
Algebra.Com's Answer #744872 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"%283%2F4%29x%2B%281%2F2%29y=5\"
\n" ); document.write( "\"%28-1%2F4%29x-%283%2F2%29y=1\"\r
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Solved by pluggable solver: Solve the System of Equations by Graphing

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\n" ); document.write( " Let's look at the first equation \"%283%2F4%29x%2B%281%2F2%29y=5\"
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\n" ); document.write( " \"4%28%283%2F4%29x%2B%281%2F2%29y%29=4%285%29\" Multiply both sides of the first equation by the LCD 4
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\n" ); document.write( " \"3x%2B2y=20\" Distribute
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\n" ); document.write( " Let's look at the second equation \"%281%2F4%29x%2B%283%2F2%29y=1\"
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\n" ); document.write( " \"4%28%281%2F4%29x%2B%283%2F2%29y%29=4%281%29\" Multiply both sides of the second equation by the LCD 4
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\n" ); document.write( " \"1x%2B6y=4\" Distribute
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\n" ); document.write( " So our new system of equations is:
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\n" ); document.write( " \"3x%2B2y=20\"
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\n" ); document.write( " \"1x%2B6y=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( " \"3x%2B2y=20\" Start with the given equation
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\n" ); document.write( " \"2y=20-3x\" Subtract \"3+x\" from both sides
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\n" ); document.write( " \"2y=-3x%2B20\" Rearrange the equation
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\n" ); document.write( " \"y=%28-3x%2B20%29%2F%282%29\" Divide both sides by \"2\"
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\n" ); document.write( " \"y=%28-3%2F2%29x%2B%2820%29%2F%282%29\" Break up the fraction
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\n" ); document.write( " \"y=%28-3%2F2%29x%2B10\" Reduce
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\n" ); document.write( " Now lets graph \"y=%28-3%2F2%29x%2B10\" (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+%28-3%2F2%29x%2B10%29+\" Graph of \"y=%28-3%2F2%29x%2B10\"
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " \"1x%2B6y=4\" Start with the given equation
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\n" ); document.write( " \"6y=4-x\" Subtract \"+x\" from both sides
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\n" ); document.write( " \"6y=-x%2B4\" Rearrange the equation
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\n" ); document.write( " \"y=%28-x%2B4%29%2F%286%29\" Divide both sides by \"6\"
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\n" ); document.write( " \"y=%28-1%2F6%29x%2B%284%29%2F%286%29\" Break up the fraction
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\n" ); document.write( " \"y=%28-1%2F6%29x%2B2%2F3\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=%28-1%2F6%29x%2B2%2F3\" to our first plot to get:
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\n" ); document.write( " Graph of \"y=%28-3%2F2%29x%2B10\"(red) and \"y=%28-1%2F6%29x%2B2%2F3\"(green)
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\n" ); document.write( " From the graph, we can see that the two lines intersect at the point (\"7\",\"-1%2F2\") (note: you might have to adjust the window to see the intersection)
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