document.write( "Question 1019408: Two numbers differ by 8, and their product is 65. Find the numbers. \n" ); document.write( "
Algebra.Com's Answer #635336 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Two numbers...
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document.write( "Let the first number = x\r\n" );
document.write( "Let the second number = y\r\n" );
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\n" ); document.write( "differ by 8,...
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document.write( "So FIRST NUMBER MINUS SECOND NUMBER EQUALS 8\r\n" );
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document.write( "That is,\r\n" );
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document.write( "x - y = 8\r\n" );
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\n" ); document.write( "and their product is 65...
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document.write( "(FIRST NUMBER) TIMES (SECOND NUMBER) EQUALS 65.\r\n" );
document.write( "xy = 65\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "\"system%28x-y=8%2Cxy=65%29\"\r\n" );
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document.write( "Solve the first equation for x\r\n" );
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document.write( "x-y = 8\r\n" );
document.write( "  x = 8+y\r\n" );
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document.write( "Substitute (8+y) for x in the second equation:\r\n" );
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document.write( "    xy = 65\r\n" );
document.write( "(8+y)y = 65\r\n" );
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document.write( "If you like, swap the two factors y and (8+y) on\r\n" );
document.write( "the left.\r\n" );
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document.write( "y(8+y) = 65\r\n" );
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document.write( "Distribute to remove parentheses:\r\n" );
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document.write( "8y+y² = 65\r\n" );
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document.write( "Swap the terms on the left\r\n" );
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document.write( "y²+8y = 65\r\n" );
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document.write( "Subtract 65 from both sides:\r\n" );
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document.write( "y²+8y-65 = 0\r\n" );
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document.write( "Factor the left sides:\r\n" );
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document.write( "(y+13)(y-5) = 0\r\n" );
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document.write( "Use the zero-factor principle:\r\n" );
document.write( "Set each factor = 0\r\n" );
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document.write( "y+13 = 0;    y-5 = 0\r\n" );
document.write( "   y = -13     y = 5\r\n" );
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document.write( "For y = -13 we substitute in the equation\r\n" );
document.write( "solved for y:\r\n" );
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document.write( "  x = 8+y\r\n" );
document.write( "  x = 8+(-13)\r\n" );
document.write( "  x = -5\r\n" );
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document.write( "So one solution is \r\n" );
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document.write( "First number = x = -5\r\n" );
document.write( "Second number = y = -13\r\n" );
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document.write( "There is another solution:\r\n" );
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document.write( "For y = 5 we substitute in the equation\r\n" );
document.write( "solved for y:\r\n" );
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document.write( "  x = 8+y\r\n" );
document.write( "  x = 8+(5)\r\n" );
document.write( "  x = 13\r\n" );
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document.write( "So the other solution is \r\n" );
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document.write( "First number = x = 13\r\n" );
document.write( "Second number = y = 5\r\n" );
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document.write( "Edwin
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