document.write( "Question 126093: Solve the system by graphing.
\n" ); document.write( " 2x + y = 4
\n" ); document.write( " x + y = 3
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Algebra.Com's Answer #92401 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( " $\"2x%2By=4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1x%2By=3\"$ \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( " $\"2x%2By=4\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=4-2x\"$ Subtract $\"2+x\"$ from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"1y=-2x%2B4\"$ Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2x%2B4%29%2F%281%29\"$ Divide both sides by $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2%2F1%29x%2B%284%29%2F%281%29\"$ Break up the fraction\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-2x%2B4\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now lets graph $\"y=-2x%2B4\"$ (note: if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B4%29+\"$ Graph of $\"y=-2x%2B4\"$ \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( " $\"1x%2By=3\"$ 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 add the graph of $\"y=-x%2B3\"$ to our first plot to get:\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B4%2C-x%2B3%29+\"$ Graph of $\"y=-2x%2B4\"$ (red) and $\"y=-x%2B3\"$ (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 ( $\"1\"$ , $\"2\"$ ) \n" ); document.write( "

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