document.write( "Question 766249: Give all solutions of each nonlinear system of equations: x^2+y^2=9, |x|=|y| \n" ); document.write( "

Algebra.Com's Answer #466860 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( " x²+y² = 9, \r\n" );
document.write( "   |x| = |y|\r\n" );
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document.write( "Square both sides of the second equation\r\n" );
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document.write( "    x² = y²\r\n" );
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document.write( "Substitute y² for x² in the first equation:\r\n" );
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document.write( " y² + y² = 9\r\n" );
document.write( "     2y² = 9\r\n" );
document.write( "      y² = \r\n" );
document.write( "       y =  =  =  =  = \r\n" );
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document.write( "And since x² = y², x also =  \r\n" );
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document.write( "So the four possible solutions are:\r\n" );
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document.write( "(,), (,), (,), (,)\r\n" );
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document.write( "All four check, so all four are solutions.\r\n" );
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document.write( "The graph of x²+y²=9 is this circle\r\n" );
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document.write( "and the graph of |y|=|x| is the pair of graphs y = |x| and y = -|x|\r\n" );
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document.write( " and\r\n" );
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document.write( "which together are\r\n" );
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document.write( "Put them together on the same graph and you get:\r\n" );
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document.write( "The four points of intersection are \r\n" );
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document.write( "(,), (,), (,), (,)\r\n" );
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document.write( "Edwin

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