document.write( "Question 430547: Please help me solve this problem by Substitution Method \"x-y=1\"
\n" ); document.write( "\"x%5E2-xy-y%5E2=-5\" I can't figure out the solution sets.\r
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Algebra.Com's Answer #299012 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "       x - y =  1\r\n" );
document.write( "x² - xy - y² = -5 \r\n" );
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document.write( "The other tutor solved the first equation for x. \r\n" );
document.write( "Just to be different I'll solve it for y:\r\n" );
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document.write( "                          x - y = 1\r\n" );
document.write( "                             -y = 1 - x\r\n" );
document.write( "                              y = -1 + x\r\n" );
document.write( "                              y = x - 1\r\n" );
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document.write( "Substitute (x - 1) for y in the second equation,\r\n" );
document.write( "but first factor -y out of the second and third terms\r\n" );
document.write( "on the left:\r\n" );
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document.write( "                   x² - xy - y² = -5\r\n" );
document.write( "                  x² - y(x + y) = -5\r\n" );
document.write( "      x² - (x - 1)[x + (x - 1)] = -5  \r\n" );
document.write( "        x² - (x - 1)(x + x - 1) = -5 \r\n" );
document.write( "           x² - (x - 1)(2x - 1) = -5\r\n" );
document.write( "            x² - (2x² - 3x + 1) = -5\r\n" );
document.write( "              x² - 2x² + 3x - 1 = -5\r\n" );
document.write( "                   -x² + 3x + 4 =  0\r\n" );
document.write( "                    x² - 3x - 4 =  0\r\n" );
document.write( "                 (x - 4)(x + 1) =  0\r\n" );
document.write( "                x - 4 = 0;  x + 1 = 0  \r\n" );
document.write( "                    x = 4       x = -1\r\n" );
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document.write( "To find the y-value for x = 4, substitute 4 for x in\r\n" );
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document.write( "                \r\n" );
document.write( "                              y = x - 1     \r\n" );
document.write( "                              y = 4 - 1\r\n" );
document.write( "                              y = 3      \r\n" );
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document.write( "So one solution is (x,y) = (4,3)\r\n" );
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document.write( "To find the y-value for x = -1, substitute -1 for x in\r\n" );
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document.write( "                \r\n" );
document.write( "                              y = x - 1     \r\n" );
document.write( "                              y = -1 - 1\r\n" );
document.write( "                              y = -2      \r\n" );
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document.write( "So the other solution is (x,y) = (-1,-2)\r\n" );
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document.write( "Edwin

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