document.write( "Question 1004970: Solve the system.
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Algebra.Com's Answer #621304 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Solve the system\r\n" );
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document.write( "x - y + z =  0   (1)\r\n" );
document.write( "x + y + z = -2   (2)\r\n" );
document.write( "x + y - z =  8   (3)\r\n" );
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document.write( "This system is special. It is possible to solve it using the mental math only.\r\n" );
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document.write( "Distract first equation from the second ((1) from (2)). You will get\r\n" );
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document.write( "2y = -2.  Hence,  y = -1.\r\n" );
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document.write( "Next, distract equation (3) from (2). You will get\r\n" );
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document.write( "2z = -10.  Hence,  z = -5.\r\n" );
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document.write( "Finally, substitute the found values y= -1 and z= -5 into the first equation. You will get\r\n" );
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document.write( "x - (-1) + (-5) = 0,   or   x = 5 - 1 = 4.\r\n" );
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document.write( "Answer.  The solution is  x= 4, y= -1 and z= -5.\r\n" );
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