document.write( "Question 48336This question is from textbook College Algebra
\n" ); document.write( ": Find all solutions of the system: (hint: factor the left side of the second equation:\r
\n" ); document.write( "\n" ); document.write( "x-y = 3
\n" ); document.write( "x^3 - y^3 = 387\r
\n" ); document.write( "\n" ); document.write( "So now after factoring I have this new system:\r
\n" ); document.write( "\n" ); document.write( "x-y = 3
\n" ); document.write( "(x-y)(x^2 + xy + y^2)= 387\r
\n" ); document.write( "\n" ); document.write( "but now how do I continue the problem?\r
\n" ); document.write( "\n" ); document.write( "Thanks for all your help! \n" ); document.write( "

Algebra.Com's Answer #31966 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

Find all solutions of the system: (hint: factor the left \r\n" );
document.write( "side of the second equation: \r\n" );
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document.write( "x-y = 3\r\n" );
document.write( "x^3 - y^3 = 387 \r\n" );
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document.write( "So now after factoring I have this new system: \r\n" );
document.write( " x-y = 3\r\n" );
document.write( "(x-y)(x² + xy + y²) = 387 \r\n" );
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document.write( "but now how do I continue the problem? \r\n" );
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document.write( "Since you have x-y = 3 you can substitute 3 for (x-y) in\r\n" );
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document.write( "          (x-y)(x² + xy + y²) = 387 \r\n" );
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document.write( "getting\r\n" );
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document.write( "              3(x² + xy + y²) = 387\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "                 x² + xy + y² = 129\r\n" );
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document.write( "Now since x-y = 3, solving for y gives\r\n" );
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document.write( "                            y = x-3\r\n" );
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document.write( "So substitute (x-3) for y in\r\n" );
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document.write( "                 x² + xy + y² = 129\r\n" );
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document.write( "         x² + x(x-3) + (x-3)² = 129\r\n" );
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document.write( "    x² + x² - 3x + (x-3)(x-3) = 129\r\n" );
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document.write( "         2x² - 3x + (x²-6x+9) = 129\r\n" );
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document.write( "       2x² - 3x + x² - 6x + 9 = 129\r\n" );
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document.write( "               3x² - 9x - 120 = 0 \r\n" );
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document.write( "              3(x² - 3x - 40) = 0 \r\n" );
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document.write( "              3(x - 8)(x + 5) = 0\r\n" );
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document.write( "That gives two possible values for x:\r\n" );
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document.write( "             x = 8 and x = -5\r\n" );
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document.write( "Now substituting x = 8 into\r\n" );
document.write( "                           \r\n" );
document.write( "                            y = x - 3\r\n" );
document.write( "                            y = 8 - 3\r\n" );
document.write( "                            y = 5\r\n" );
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document.write( "So one solution is (x, y) = (8, 5)  \r\n" );
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document.write( "Substituting x = -5 into\r\n" );
document.write( "                           \r\n" );
document.write( "                            y = x - 3\r\n" );
document.write( "                            y = -5 - 3\r\n" );
document.write( "                            y = -8\r\n" );
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document.write( "So the other solution is (x, y) = (-5, -8) \r\n" );
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document.write( "Edwin

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