document.write( "Question 1203611: x+4y-6z=-1
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Algebra.Com's Answer #839307 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "You are given this system of three linear equations \r\n" );
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document.write( "    x  + 4y - 6z = -1    (1)\r\n" );
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document.write( "   2x  -  y + 2z = -7    (2)\r\n" );
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document.write( "   -x  + 2y - 4z =  5    (3)\r\n" );
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document.write( "Quick inspection shows that the part  \"-y + 2z\"  in equation (2) and the part \"2y - 4z\" in equation (3)\r\n" );
document.write( "fit very well for mutual destruction. So, you multiply equation (2) by 2 and add it with equation (3).\r\n" );
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document.write( "The modified equations are\r\n" );
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document.write( "    4x - 2y + 4z = -14   (2')\r\n" );
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document.write( "   -x  + 2y - 4z =  5    (3')\r\n" );
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document.write( "After adding these equations, you get\r\n" );
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document.write( "    3x           = -14 + 5 = 9,  which implies  x = -9/3 = -3, so one unknown is just found.\r\n" );
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document.write( "Now you plug in x= -3 into equations (1) and (3). You get a system of two equations\r\n" );
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document.write( "    -3    + 4y - 6z = -1    (1'')\r\n" );
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document.write( "    -(-3) + 2y - 4z = 5     (3'')\r\n" );
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document.write( "You simplify these equations further\r\n" );
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document.write( "     4y - 6z = 2            (1''')\r\n" );
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document.write( "     2y - 4z = 2            (3''')\r\n" );
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document.write( "Next you divide all the term in (1''') by 2, keeping (3''') as is.  You get\r\n" );
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document.write( "     2y - 3z = 1            (1'''')\r\n" );
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document.write( "     2y - 4z = 2            (3'''')\r\n" );
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document.write( "Next you subtract equation (3'''') from equation (1'''').   You get then\r\n" );
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document.write( "           z = 1 - 2 = -1.    Thus, one more unknown is found.\r\n" );
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document.write( "To find the last unknown, y, use equation (1''''). Substitute there z= -1 to get\r\n" );
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document.write( "    2y - 3*(-1) = 1,  and  obtain  then  2y + 3 = 1,  2y = 1 - 3 = -2,  y= -2/2 = -1.\r\n" );
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document.write( "ANSWER.  x= -3;  y= -1;  z= -1.\r\n" );
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