document.write( "Question 1208774: Solve each system by elimination.
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\n" ); document.write( "x+y+z=-2
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Algebra.Com's Answer #847221 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " x +  y + z =  -2    (1)\r\n" );
document.write( "2x + 2y - 3z = 11    (2)\r\n" );
document.write( "3x -  y +  z =  4    (3)\r\n" );
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document.write( "You are exceptionally lucky person, because in this case the solution \r\n" );
document.write( "of the given system is very easy.\r\n" );
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document.write( "Multiply equation (1) by 2 (both sides); then subtract from equation (2).\r\n" );
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document.write( "You will get then  \r\n" );
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document.write( "    -3z - 2z = 11 - 2*(-2)\r\n" );
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document.write( "    - 5z = 15\r\n" );
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document.write( "       z = 15/(-5) = -3.\r\n" );
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document.write( "   +---------------------------------------+\r\n" );
document.write( "   |  First elimination step is complete.  |\r\n" );
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document.write( "Now substitute z= -3 into equations (1) and (3).  You will get then\r\n" );
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document.write( "    x +  y + (-3) = -2    (4)\r\n" );
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document.write( "    3x - y + (-3) =  4    (5)\r\n" );
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document.write( "Add equations (4) and (5).  You will get\r\n" );
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document.write( "    4x + (-6) = 2  --->  4x - 6 = 2  --->  4x = 2 + 6 = 8  --->  x = 8/4 = 2.\r\n" );
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document.write( "   +----------------------------------------+\r\n" );
document.write( "   |  Second elimination step is complete.  |\r\n" );
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document.write( "Now substitute x= 2 and z= -3 into equation (1).  You will get\r\n" );
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document.write( "    2 + y + (-3) = -2  --->  y = -2 - 2 + 3 = -1.\r\n" );
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document.write( "ANSWER.  The solution is  x= 2,  y= -1,  z= -3.\r\n" );
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document.write( "To check, substitute these values to each equation  and make sure that left sides are equal to right sides.\r\n" );
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