document.write( "Question 555378: 2x+y=5
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Algebra.Com's Answer #361758 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%2By=5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3x-y=10\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to graph these equations, we need to solve for y for each equation.\r
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\n" ); document.write( "\n" ); document.write( "So let's solve for y on the first equation\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%2By=5\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=5-2x\"$ Subtract $\"2+x\"$ from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=-2x%2B5\"$ Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2x%2B5%29%2F%281%29\"$ Divide both sides by $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2%2F1%29x%2B%285%29%2F%281%29\"$ Break up the fraction\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-2x%2B5\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now lets graph $\"y=-2x%2B5\"$ (note: if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B5%29+\"$ Graph of $\"y=-2x%2B5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So let's solve for y on the second equation\r
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\n" ); document.write( "\n" ); document.write( " $\"3x-y=10\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"-y=10-3x\"$ Subtract $\"3+x\"$ from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"-y=-3x%2B10\"$ Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-3x%2B10%29%2F%28-1%29\"$ Divide both sides by $\"-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-3%2F-1%29x%2B%2810%29%2F%28-1%29\"$ Break up the fraction\r
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\n" ); document.write( "\n" ); document.write( " $\"y=3x-10\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now lets add the graph of $\"y=3x-10\"$ to our first plot to get:\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B5%2C3x-10%29+\"$ Graph of $\"y=-2x%2B5\"$ (red) and $\"y=3x-10\"$ (green)\r
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\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the two lines intersect at the point ( $\"3\"$ , $\"-1\"$ ) \n" ); document.write( "

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