document.write( "Question 1069418: Solving systemn of equations in three variables\r
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Algebra.Com's Answer #684619 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( " $\"highlight%28cross%28Solving%29%29\"$ Solve $\"highlight%28cross%28systemn%29%29\"$ system of equations in three variables\r
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\n" ); document.write( "-x+2y+z=1\r
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\n" ); document.write( "\n" ); document.write( "thank you
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document.write( " x -  y -  z = 0,    (1)\r\n" );
document.write( "2x - 3y + 2z = 7,    (2)\r\n" );
document.write( "-x + 2y +  z = 1.    (3)\r\n" );
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document.write( "Add equations (1) and (3). You will get \r\n" );
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document.write( "0x +  y + 0z = 1,    or simply   y = 1.\r\n" );
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document.write( "So, you just found one unknown: y = 1.\r\n" );
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document.write( "Now substitute this value of y into equations (1) and (2):\r\n" );
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document.write( " x -   1 -  z = 0,   (4)\r\n" );
document.write( "2x - 3*1 + 2z = 7.   (5)\r\n" );
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document.write( "Simplify it and write it in canonical form:\r\n" );
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document.write( "  x -  z =  1,       (4')\r\n" );
document.write( "2x  + 2z = 10.       (5')\r\n" );
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document.write( "Divide (5') by 2 (both sides).\r\n" );
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document.write( "You will get the system (4'),(5') in the form\r\n" );
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document.write( "  x -  z =  1,       (4'')\r\n" );
document.write( "  x  + z =  5.       (5'')\r\n" );
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document.write( "Now, add equations (4'') and (5''). You will get\r\n" );
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document.write( "  2x = 6   --->  x = 3.\r\n" );
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document.write( "I leave it to you to find the last remaining unknown z.\r\n" );
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