document.write( "Question 121261: Here is the problem\r
\n" ); document.write( "\n" ); document.write( "11. x + y = 5
\n" ); document.write( " x-y = 1 \r
\n" ); document.write( "\n" ); document.write( "I understand how they got the point on the graph. What I don't understand is how they got this answer. (3,2)
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Algebra.Com's Answer #88965 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"x+%2B+y+=+5\"$ ЕЕЕЕЕЕЕЕЕ..(1)\r
\n" ); document.write( "\n" ); document.write( " $\"x-y+=+1\"$ ЕЕЕЕЕЕЕЕЕ..(2)\r
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\n" ); document.write( "\n" ); document.write( "Solve this system:\r
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\n" ); document.write( "\n" ); document.write( " $\"x+%2B+y+=+5\"$ ЕЕЕЕЕЕЕЕЕ..(1)Е =>Е $\"x+=+-y+%2B+5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-y+=+1\"$ ЕЕЕЕЕЕЕЕЕ..(2)Еsubstitute $\"x\"$ and find $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-y+%2B+5+-y+=+1\"$ ЕЕЕЕЕЕЕЕЕ..(2)\r
\n" ); document.write( "\n" ); document.write( " $\"-2y+=+1+-+5\"$ Е\r
\n" ); document.write( "\n" ); document.write( " $\"-2y+=++-+4\"$ ЕЕЕdivide both sides by $\"-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y+=++2\"$ ЕЕЕ\r
\n" ); document.write( "\n" ); document.write( "=>Е $\"x+=+-y+%2B+5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-2+%2B+5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( "So, the point is ( $\"3\"$ , $\"2\"$ ) and it is intersection of these two lines\r
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\n" ); document.write( "\n" ); document.write( "here is the graph:\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( " $\"1x%2By=5\"$
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\n" ); document.write( " $\"1x-y=1\"$
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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( " $\"1x%2By=5\"$ Start with the given equation
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\n" ); document.write( " $\"1y=5-x\"$ Subtract $\"+x\"$ from both sides
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\n" ); document.write( " $\"1y=-x%2B5\"$ Rearrange the equation
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\n" ); document.write( " $\"y=%28-x%2B5%29%2F%281%29\"$ Divide both sides by $\"1\"$
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\n" ); document.write( " $\"y=%28-1%2F1%29x%2B%285%29%2F%281%29\"$ Break up the fraction
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\n" ); document.write( " $\"y=-x%2B5\"$ Reduce
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\n" ); document.write( " Now lets graph $\"y=-x%2B5\"$ (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B5%29+\"$ Graph of $\"y=-x%2B5\"$
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " $\"1x-y=1\"$ Start with the given equation
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\n" ); document.write( " $\"-y=1-x\"$ Subtract $\"+x\"$ from both sides
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\n" ); document.write( " $\"-y=-x%2B1\"$ Rearrange the equation
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\n" ); document.write( " $\"y=%28-x%2B1%29%2F%28-1%29\"$ Divide both sides by $\"-1\"$
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\n" ); document.write( " $\"y=%28-1%2F-1%29x%2B%281%29%2F%28-1%29\"$ Break up the fraction
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\n" ); document.write( " $\"y=x-1\"$ Reduce
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\n" ); document.write( " Now lets add the graph of $\"y=x-1\"$ to our first plot to get:
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\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B5%2Cx-1%29+\"$ Graph of $\"y=-x%2B5\"$ (red) and $\"y=x-1\"$ (green)
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\n" ); document.write( " From the graph, we can see that the two lines intersect at the point ( $\"3\"$ , $\"2\"$ ) (note: you might have to adjust the window to see the intersection)

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