document.write( "Question 144394: x+y=3
\n" ); document.write( "x-y=5 \n" ); document.write( "

Algebra.Com's Answer #105139 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "Start with the given system of equations:\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%2By=3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1x-y=5\"$ \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( " $\"1x%2By=3\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=3-x\"$ Subtract $\"+x\"$ from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=-x%2B3\"$ Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-x%2B3%29%2F%281%29\"$ Divide both sides by $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%2F1%29x%2B%283%29%2F%281%29\"$ Break up the fraction\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%2B3\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now lets graph $\"y=-x%2B3\"$ (note: if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B3%29+\"$ Graph of $\"y=-x%2B3\"$ \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( " $\"1x-y=5\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"-y=5-x\"$ Subtract $\"+x\"$ from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"-y=-x%2B5\"$ Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-x%2B5%29%2F%28-1%29\"$ Divide both sides by $\"-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%2F-1%29x%2B%285%29%2F%28-1%29\"$ Break up the fraction\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x-5\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now lets add the graph of $\"y=x-5\"$ to our first plot to get:\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B3%2Cx-5%29+\"$ Graph of $\"y=-x%2B3\"$ (red) and $\"y=x-5\"$ (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 ( $\"4\"$ , $\"-1\"$ ) \n" ); document.write( "

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