document.write( "Question 524087: Can you help solve these functions with 3 variables?\r
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\n" ); document.write( "2a+ b - 5c = -11
\n" ); document.write( "a - 2b + 3c = 6 \n" ); document.write( "
Algebra.Com's Answer #347563 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "eq. 1       4a + 2b -  c =   5\r\n" );
document.write( "eq. 2       2a +  b - 5c = -11\r\n" );
document.write( "eq. 3        a - 2b + 3c =   6\r\n" );
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document.write( "You can eliminate b immediately from eqs. 1 and 3 by adding them\r\n" );
document.write( "vertically term-by-term:\r\n" );
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document.write( "eq. 1       4a + 2b -  c =   5\r\n" );
document.write( "eq. 3        a - 2b + 3c =   6\r\n" );
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document.write( "eq. 4       5a      + 2c =  11\r\n" );
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document.write( "So we must eliminate be from another pair of equations:\r\n" );
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document.write( "We multiply eq. 2 through by 2 \r\n" );
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document.write( "            4a + 2b - 10c = -22\r\n" );
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document.write( "so we can add eq. 3 to it and eliminate b from that pair:\r\n" );
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document.write( "            4a + 2b - 10c = -22\r\n" );
document.write( "eq. 3        a - 2b +  3c =   6\r\n" );
document.write( "            -------------------\r\n" );
document.write( "eq. 5       5a      -  7c = -16\r\n" );
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document.write( "Now we take eqs. 4 and 5 together as a system of two equations in two\r\n" );
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document.write( "eq. 4       5a + 2c =  11\r\n" );
document.write( "eq. 5       5a - 7c = -16\r\n" );
document.write( "   \r\n" );
document.write( "We multiply eq. 5 by -1 \r\n" );
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document.write( "           -5a + 7c = 16\r\n" );
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document.write( "so we can add eq. 4 to it to eliminate \"a\":\r\n" );
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document.write( "           -5a + 7c = 16\r\n" );
document.write( "eq. 4       5a + 2c = 11\r\n" );
document.write( "          ----------------\r\n" );
document.write( "                 9c = 27\r\n" );
document.write( "                  c = 3\r\n" );
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document.write( "Substitute c = 3 in eq. 4\r\n" );
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document.write( "          5a + 2(3) =  11\r\n" );
document.write( "             5a + 6 = 11\r\n" );
document.write( "                 5a = 5\r\n" );
document.write( "                  a = 1\r\n" );
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document.write( "Substitute c = 3 and a = 1 in eq. 3\r\n" );
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document.write( "    (1) - 2b + 3(3) =   6\r\n" );
document.write( "         1 - 2b + 9 = 6\r\n" );
document.write( "            10 - 2b = 6\r\n" );
document.write( "                -2b = -4\r\n" );
document.write( "                  b = 2\r\n" );
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document.write( "So the solution is (a,b,c) = (1,2,3)\r\n" );
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document.write( "Edwin

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