document.write( "Question 1058629: 2. Two numbers are such that if the square of the first number is subtracted by twice their product, the difference is -1. But twice the product added to the sum of thrice the square of the first number and five times that number gives 10. \n" ); document.write( "
Algebra.Com's Answer #673789 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
2. Two numbers
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document.write( "x = first number\r\n" );
document.write( "y = second number\r\n" );
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\n" ); document.write( "are such that if the square of the first number
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document.write( "The square of the first number is x2\r\n" );
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\n" ); document.write( "is subtracted from twice their product,
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document.write( "Twice their product is 2xy\r\n" );
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document.write( "So we subtract x2 from 2xy\r\n" );
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document.write( "That's 2xy - x2\r\n" );
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\n" ); document.write( "the difference is -1.
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document.write( "So we set that difference (subtraction) equal to -1 \r\n" );
document.write( "and that's our first equation:\r\n" );
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document.write( "2xy - x2 = -1\r\n" );
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\n" ); document.write( "But twice the product
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document.write( "That's xy\r\n" );
document.write( "

\n" ); document.write( "added to the sum of thrice the square of the first number
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document.write( "that's 3x2\r\n" );
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\n" ); document.write( "and five times that number
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document.write( "that's 5x\r\n" );
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document.write( "So the sum of those is 3x2 + 5x\r\n" );
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\n" ); document.write( "gives 10
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document.write( "So we add xy to that, which is 3x2 + 5x + xy \r\n" );
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document.write( "and we set that = 10, and the second equation is\r\n" );
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document.write( "3x2 + 5x + xy = 10 \r\n" );
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document.write( "So the system of equations is\r\n" );
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document.write( "\"system%282xy+-+x%5E2+=+-1%2C+3x%5E2+%2B+5x+%2B+xy+=+10%29\" \r\n" );
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document.write( "That has solutions:\r\n" );
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document.write( "\"x+=+%28-5+-+2sqrt%2843%29%29%2F7\", \"y+=+%28-10+-+2sqrt%2843%29%29%2F21\"\r\n" );
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document.write( "and\r\n" );
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document.write( "\"x+=+%28-5+%2B+2sqrt%2843%29%29%2F7\", \"y+=+%28-10+%2B+2sqrt%2843%29%29%2F21\"\r\n" );
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document.write( "Edwin
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