document.write( "Question 964057: Please help me to solve this: a+3b+2c=3, 2a-b-3c=-8, 5a+2b+c=9 solve for a
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Algebra.Com's Answer #588946 by Edwin McCravy(20056)\"\" \"About 
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\"system%28a%2B3b%2B2c=3%2C++2a-b-3c=-8%2C++5a%2B2b%2Bc=9%29\"
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document.write( "There are at least 6 different methods to solve systems of equations.\r\n" );
document.write( "You will always get the same answer regardless of which of the methods you use.\r\n" );
document.write( "I have no way of know which of the 6 methods you are studying.\r\n" );
document.write( "The six different methods are\r\n" );
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document.write( "1. Substitution\r\n" );
document.write( "2. Elimination\r\n" );
document.write( "3. Gaussian elimination\r\n" );
document.write( "4. Cramer's rule\r\n" );
document.write( "5. Gauss-Jordan matrix method\r\n" );
document.write( "6. Inverse matrix method\r\n" );
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document.write( "I used only the most basic one, substitution.  That may or may not be the\r\n" );
document.write( "method you are studying, nor the easiest, but you can certainly understand it,\r\n" );
document.write( "because it is very much like the substitution method when there are only\r\n" );
document.write( "2 equations and 2 unknowns.\r\n" );
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document.write( "1. Solve the first equation for \"a\".\r\n" );
document.write( "2. Substitute the expression that you get for \"a\" in the other two equations.\r\n" );
document.write( "   That gives you two equations in only \"b\" and \"c\".\r\n" );
document.write( "3. Solve one of those for b.\r\n" );
document.write( "4. Substitute the expression that you get for \"b\" in the second equation.\r\n" );
document.write( "   That gives you one equation in only \"c\".\r\n" );
document.write( "5. Solve that and get the value for \"c\"\r\n" );
document.write( "6. Substitute that value for \"c\" in one of the equations in only \"b\" and \"c\".  \r\n" );
document.write( "7. Solve that and get the value for \"b\".\r\n" );
document.write( "8. Substitute the values for \"b\" and\"c\" in one of the original equations.\r\n" );
document.write( "9. Solve for \"a\".\r\n" );
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document.write( "1. a+3b+2c = 3\r\n" );
document.write( "         a = 3-3b-2c\r\n" );
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document.write( "2.         2a-b-3c = -8\r\n" );
document.write( "   2(3-3b-2c)-b-3c = -8\r\n" );
document.write( "      6-6b-4c-b-3c = -8\r\n" );
document.write( "           6-7b-7c = -8\r\n" );
document.write( "            -7b-7c = -14   <--divide through by -7\r\n" );
document.write( "               b+c = 2\r\n" );
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document.write( "           5a+2b+c = 9\r\n" );
document.write( "   5(3-3b-2c)+2b+c = 9\r\n" );
document.write( "   15-15b-10c+2b+c = 9\r\n" );
document.write( "         15-13b-9c = 9\r\n" );
document.write( "           -13b-9c = -6 \r\n" );
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document.write( "3.             b+c = 2\r\n" );
document.write( "                 b = 2-c\r\n" );
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document.write( "4.         -13b-9c = -6\r\n" );
document.write( "       -13(2-c)-9c = -6\r\n" );
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document.write( "5.      -26+13c-9c = -6\r\n" );
document.write( "            -26+4c = -6\r\n" );
document.write( "                4c = 20\r\n" );
document.write( "                 c = 5  \r\n" );
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document.write( "6.              b+c = 2\r\n" );
document.write( "                b-5 = 2\r\n" );
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document.write( "7.              b+5 = 2\r\n" );
document.write( "                  b = -3\r\n" );
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document.write( "8.     a+3b+2c = 3\r\n" );
document.write( "  a+3(-3)+2(5) = 3\r\n" );
document.write( "        a-9+10 = 3\r\n" );
document.write( "           a+1 = 3\r\n" );
document.write( "             a = 2\r\n" );
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document.write( "The solution is a=2, b=-3, c=5.\r\n" );
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document.write( "Sometimes that is written (a,b,c) = (2,-3,5)     \r\n" );
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document.write( "Edwin
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