document.write( "Question 113829: 10. Solve the following system both by graphing and then check result algebraically.
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\n" ); document.write( "2y = x^2
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Algebra.Com's Answer #82837 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First let's graph $\"y=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=8\"$ , simply draw a horizontal line through the y=8\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+8%29+\"$ Graph of $\"y=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's move onto the second equation $\"2y=x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2y=x%5E2\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2%2F2\"$ Divide both sides by 2 to solve for y\r
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\n" ); document.write( "\n" ); document.write( "Now let's graph $\"y=x%5E2%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to do so, let's make a table by plugging in x-values (you get to choose which ones) to find the y-values\r
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document.write( "       x          y\r\n" );
document.write( "   -5.00000   12.50000\r\n" );
document.write( "   -4.00000    8.00000\r\n" );
document.write( "   -3.00000    4.50000\r\n" );
document.write( "   -2.00000    2.00000\r\n" );
document.write( "   -1.00000    0.50000\r\n" );
document.write( "    0.00000    0.00000\r\n" );
document.write( "    1.00000    0.50000\r\n" );
document.write( "    2.00000    2.00000\r\n" );
document.write( "    3.00000    4.50000\r\n" );
document.write( "    4.00000    8.00000\r\n" );
document.write( "    5.00000   12.50000\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now let's plot these points and connect them to get this graph\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2F2%29+\"$ Graph of $\"y=x%5E2%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's plot the two graphs together:\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C8%2C+x%5E2%2F2%29+\"$ Graph of $\"y=8\"$ (red) $\"y=x%5E2%2F2\"$ (green)\r
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\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the two lines intersect at x=-4 and x=4 which means the solutions are (-4,8) or (4,8)\r
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\n" ); document.write( "\n" ); document.write( "Now let's solve algebraically:\r
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\n" ); document.write( "\n" ); document.write( "Start with the given system\r
\n" ); document.write( "\n" ); document.write( " $\"y=8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2y=x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2%288%29=x%5E2\"$ Take the 2nd equation and plug in $\"y=8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"16=x%5E2\"$ Multiply\r
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Take the square root of both sides\r
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\n" ); document.write( "\n" ); document.write( "So we then get $\"x=-4\"$ or $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this means our solutions are (-4,8) or (4,8) (remember y is always 8 since the first equation is $\"y=8\"$ )\r
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