document.write( "Question 1029154: Hi, Can anyone solve this problem? The sum of three numbers is 9. The first minus the second, plus the third is 3. The first minus the third is 1 more than the second. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #644176 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Hi, Can anyone solve this problem? The sum of three numbers is 9. The first minus the second, plus the third is 3.
\n" ); document.write( "The first minus the third is 1 more than the second. What are the numbers?
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document.write( "What you are given is \r\n" );
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document.write( "x + y + z = 9,    (1)\r\n" );
document.write( "x - y + z = 3,    (2)\r\n" );
document.write( "x - z = y + 1.    (3)\r\n" );
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document.write( "Modify (3):\r\n" );
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document.write( "x - y - z = 1.    (3')\r\n" );
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document.write( "Add equations (1) and (3') (both sides). You will get\r\n" );
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document.write( "2x = 9 + 1,   or   2x = 10,   hence,   x =  = 5.\r\n" );
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document.write( "Add equations (1) and (2). You will get\r\n" );
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document.write( "2x + 2z = 12.      (4)\r\n" );
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document.write( "Since x = 5, it gives 2*5 + 2z = 12,   or   2z = 12 - 10,   or 2z = 2,   and then  z = 1.\r\n" );
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document.write( "Finally, from (1) y = 9 - x - z = 9 - 5 - 1 = 3.\r\n" );
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document.write( "Answer.  x = 5,  y = 3  and  z = 1.\r\n" );
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document.write( "Check it yourself.\r\n" );
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