document.write( "Question 787879: How do you solve these equations ? I'm trying to find linear systems in three variables .
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Algebra.Com's Answer #478361 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. Pick a letter to eliminate\r\n" );
document.write( "2. Pick 2 equations to eliminate that letter from\r\n" );
document.write( "3. Pick one of those equations with the third equation and eliminate\r\n" );
document.write( "   that SAME letter from.\r\n" );
document.write( "4. Solve the resulting system of two equations in two unknowns.\r\n" );
document.write( "5. Substitute those values in one of the original equations to\r\n" );
document.write( "   find the first letter eliminated.\r\n" );
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document.write( "(1)     -x +  y + 2z = 7 \r\n" );
document.write( "(2)     2x + 3y +  z = 1 \r\n" );
document.write( "(3)    -3x - 4y +  z = 4\r\n" );
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document.write( "1. Pick a letter to eliminate.\r\n" );
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document.write( "I'll pick z\r\n" );
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document.write( "2. Pick 2 equations to eliminate that letter from\r\n" );
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document.write( "I'll pick (2) and (3):\r\n" );
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document.write( "(2)     2x + 3y +  z = 1 \r\n" );
document.write( "(3)    -3x - 4y +  z = 4\r\n" );
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document.write( "I'll multiply (2) by -1 and add (3) to it\r\n" );
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document.write( "       -2x - 3y -  z = -1 \r\n" );
document.write( "(3)    -3x - 4y +  z =  4\r\n" );
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document.write( "(4)    -5x - 7y      =  3\r\n" );
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document.write( "3. Pick one of those equations with the third equation and eliminate\r\n" );
document.write( "   that SAME letter from.\r\n" );
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document.write( "I'll pick (2) and use it with (1) to eliminate the SAME letter z\r\n" );
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document.write( "(1)     -x +  y + 2z = 7 \r\n" );
document.write( "(2)     2x + 3y +  z = 1\r\n" );
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document.write( "I'll multiply (2) by -2 and add it to (1)\r\n" );
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document.write( "(1)     -x +  y + 2z =  7 \r\n" );
document.write( "       -4x - 6y - 2z = -2\r\n" );
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document.write( "(5)    -5x - 5y      =  5\r\n" );
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document.write( "4. Solve the resulting system of two equations in two unknowns.\r\n" );
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document.write( "(4)    -5x - 7y = 3\r\n" );
document.write( "(5)    -5x - 5y = 5\r\n" );
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document.write( "Multiply (4) by -1 and add (5) to it:\r\n" );
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document.write( "        5x + 7y = -3\r\n" );
document.write( "(5)    -5x - 5y =  5\r\n" );
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document.write( "             2y =  2\r\n" );
document.write( "              y =  1\r\n" );
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document.write( "Substitute y = 1 in (4) to find x\r\n" );
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document.write( "(4)    -5x - 7y = 3\r\n" );
document.write( "     -5x - 7(1) = 3\r\n" );
document.write( "        -5x - 7 = 3\r\n" );
document.write( "            -5x = 10\r\n" );
document.write( "              x = -2\r\n" );
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document.write( "5. Substitute those values in one of the original equations to\r\n" );
document.write( "   find the first letter eliminated.\r\n" );
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document.write( "I'll substitute x = -2 and y = 1 in (2)\r\n" );
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document.write( "(2)     2x + 3y +  z = 1\r\n" );
document.write( "    2(-2) + 3(1) + z = 1\r\n" );
document.write( "          -4 + 3 + z = 1\r\n" );
document.write( "              -1 + z = 1\r\n" );
document.write( "                   z = 2\r\n" );
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document.write( "(x,y,z) = (-2,1,2)\r\n" );
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document.write( "Notice that different people would pick different letters\r\n" );
document.write( "and diferent equations but in the end the solutions would\r\n" );
document.write( "all be the same.\r\n" );
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document.write( "Also sometimes the process can be shortened because one of\r\n" );
document.write( "the letters is already eliminated from one of the equations.\r\n" );
document.write( "But that was not the case here because all three equations\r\n" );
document.write( "cntained all three letters.\r\n" );
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document.write( "Edwin
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