document.write( "Question 1089003: The sum of three numbers is 11. The sum of twice the first number,
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Algebra.Com's Answer #703334 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The sum of three numbers is 11.  \r\n" );
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document.write( "X + Y + Z = 11\r\n" );
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document.write( "The sum of twice the first number,  4 times the second number, \r\n" );
document.write( "and 5 times the third number is 30.  \r\n" );
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document.write( "2X + 4Y + 5Z = 30\r\n" );
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document.write( "The difference between 6 times the first number and the second number \r\n" );
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document.write( "6X - Y = 47\r\n" );
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document.write( "So the system is \r\n" );
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document.write( "(eq. 1)    X +  Y +  Z = 11\r\n" );
document.write( "(eq. 2)   2X + 4Y + 5Z = 30\r\n" );
document.write( "(eq. 3)   6X -  Y      = 47\r\n" );
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document.write( "Since Z is already eliminated from (eq. 3), we\r\n" );
document.write( "eliminate Z from the other two equations by\r\n" );
document.write( "multiplying (eq. 1) by -5 and adding to (eq. 2)\r\n" );
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document.write( "         -5X - 5Y - 5Z = -55\r\n" );
document.write( "(eq. 2)   2X + 4Y + 3Z =  30\r\n" );
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document.write( "(eq. 4)  -3X - Y       = -25\r\n" );
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document.write( "Now multiply (eq. 3) by -1 and add (eq. 4)\r\n" );
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document.write( "(eq. 3)   6X - Y       =  47\r\n" );
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document.write( "         -6X + Y       = -47\r\n" );
document.write( "(eq. 4)  -3X - Y       = -25\r\n" );
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document.write( "(eq. 5)  -9X           = -72\r\n" );
document.write( "           X           =   8\r\n" );
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document.write( "Substitute 8 for X in (eq. 4)\r\n" );
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document.write( "(eq. 4)  -3X - Y       = -25\r\n" );
document.write( "       -3(8) - Y       = -25\r\n" );
document.write( "        -24  - Y       = -25\r\n" );
document.write( "              -Y       =  -1\r\n" );
document.write( "               Y       =   1   \r\n" );
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document.write( "Substitute 8 for X and 1 for Y in (eq. 1)\r\n" );
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document.write( "(eq. 1)    X +  Y +  Z = 11\r\n" );
document.write( "           8 +  1 +  Z = 11\r\n" );
document.write( "                9 +  Z = 11\r\n" );
document.write( "                     Z = 2\r\n" );
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document.write( "So the solution is (X,Y,Z) = (8,1,2)\r\n" );
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document.write( "Edwin
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