document.write( "Question 1167063: so Im trying to brush up on my skills and have been presented with: \r
\n" ); document.write( "\n" ); document.write( "x - y - z = 5
\n" ); document.write( "y - x - z = 1
\n" ); document.write( "z - y - x = -15
\n" ); document.write( "x * y - z = a \r
\n" ); document.write( "\n" ); document.write( "so far all I can remember is to equal everything out to zero leaving: \r
\n" ); document.write( "\n" ); document.write( "x - y - z - 5 = 0
\n" ); document.write( "y - x - z - 1 = 0
\n" ); document.write( "z - y - x + 15 = 0
\n" ); document.write( "x * y - z - a = 0\r
\n" ); document.write( "\n" ); document.write( "what kind of problem is this exactly and how do I solve he variables? \n" ); document.write( "
Algebra.Com's Answer #791644 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x - y - z = 5        (1)\r\n" );
document.write( "y - x - z = 1        (2)\r\n" );
document.write( "z - y - x = -15      (3)\r\n" );
document.write( "x * y - z = a        (4)\r\n" );
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document.write( "The problem is to find three unknowns x, y and z  from equations (1), (2) and (3)\r\n" );
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document.write( "and THEN (=after that) to find the value of \"a\" from equation (4).\r\n" );
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document.write( "The system of three equations (1), (2) and (3) is VERY SPECIAL, and there is  VERY SPECIAL trick to solve it.\r\n" );
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document.write( "Add equations (1), (2) and (3) (=add separately their left and right sides). You will get then\r\n" );
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document.write( "    (x+y+z) - 2x - 2y - 2z = 5+1-15,   or\r\n" );
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document.write( "     -x - y - z = -9,                  or\r\n" );
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document.write( "      x + y + z = 9.     (5)\r\n" );
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document.write( "Now add equations (1) and (5). You will get  \r\n" );
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document.write( "     2x         = 5+9 = 14;  hence,  x = 14/2 = 7.\r\n" );
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document.write( "Next, add equations (2) and (5). You will get  \r\n" );
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document.write( "    2y          = 1 + 9 = 10;  hence,  y = 10/2 = 5.\r\n" );
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document.write( "Finally, add equations (3) and (5). You will get  \r\n" );
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document.write( "    2z          = -15 + 9 = -6;  hence,  y = -6/2 = -3.\r\n" );
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document.write( "Thus  x= 7,  y= 5,  z= -3.\r\n" );
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document.write( "Hence,  a = x*y - z = 7*5 - (-3) = 35 + 3 = 38.\r\n" );
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document.write( "ANSWER.  x= 7,  y= 5,  z= -3,  a = 38.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "There are TWO MAJOR LESSONS for you to learn from my solution.\r
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document.write( "    First is to read the problem attentively and to understand what they want from you.\r\n" );
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document.write( "    Second is this SPECIAL TRICK to solve the given system of equations.\r\n" );
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