document.write( "Question 26453: 
Solve for a, b, and c using addition-subtraction method \r\n" );
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document.write( " a - 3b -  c = 10 \r\n" );
document.write( "5a - 2b + 2c = 6 \r\n" );
document.write( "3a + 2b +  c = 13
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Algebra.Com's Answer #14291 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve for a, b, and c using addition-subtraction method \r\n" );
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document.write( " a - 3b -  c = 10 \r\n" );
document.write( "5a - 2b + 2c = 6 \r\n" );
document.write( "3a + 2b +  c = 13\r\n" );
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document.write( "To solve a system of 3 equations in 3 unknowns using the \r\n" );
document.write( "addition-subtraction.\r\n" );
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document.write( "Case 1. When one of the equations contains only one unknown.\r\n" );
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document.write( "Solve for the unknown in that equation.  Substitute its value\r\n" );
document.write( "in the other two equations and you have two equations and two\r\n" );
document.write( "unknowns.  Solve that system of two equations in two unknowns.\r\n" );
document.write( "Thios will give you the other two unknowns.\r\n" );
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document.write( "Case 2.  When one of the equations contains only two unknowns.\r\n" );
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document.write( "Pick one of the equations with only two unknowns.\r\n" );
document.write( "Observe which unknown is missing in it.\r\n" );
document.write( "Eliminate that unknown from the other two equations\r\n" );
document.write( "This gives you a second equation with the same two unknowns as the one\r\n" );
document.write( "    you picked.\r\n" );
document.write( "Solve this system for those two unknowns.\r\n" );
document.write( "Substitute these values in one of the original three equations which\r\n" );
document.write( "contains the remaining unknown and solve to find its value.\r\n" );
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document.write( "Case 3.  When all three equations contain three unknowns\r\n" );
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document.write( "Pick any pair of equations and eliminate an unmnown.\r\n" );
document.write( "Pick a different pair of equations and eliminate THAT VERY SAME UNKNOWN.   \r\n" );
document.write( "This gives you two equations in two unknowns.\r\n" );
document.write( "Solve for those two unknowns.\r\n" );
document.write( "Substitute these values in any one of the original equations and solve\r\n" );
document.write( "    for the third unknown.\r\n" );
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document.write( " a - 3b -  c = 10 \r\n" );
document.write( "5a - 2b + 2c = 6 \r\n" );
document.write( "3a + 2b +  c = 13\r\n" );
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document.write( "This is case 3 because all three equations contain all three unknowns.\r\n" );
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document.write( "Pick any pair of equations and eliminate an unmnown.\r\n" );
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document.write( "       Pick the 1st and 3rd and eliminate c\r\n" );
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document.write( "                     a - 3b -  c = 10 \r\n" );
document.write( "                    3a + 2b +  c = 13\r\n" );
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document.write( "       Add them and the c's will cancel:\r\n" );
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document.write( "                    4a -  b      = 23 \r\n" );
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document.write( "Pick a different pair of eqwuations and eliminate THAT VERY SAME UNKNOWN.\r\n" );
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document.write( "       Pick the 1st and 2nd and eliminate c\r\n" );
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document.write( "                     a - 3b -  c = 10 \r\n" );
document.write( "                    5a - 2b + 2c = 6\r\n" );
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document.write( "       Multiply ther first equationm thru by 2 so the c's will cancel:\r\n" );
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document.write( "                    2a - 6b - 2c = 20 \r\n" );
document.write( "                    5a - 2b + 2c = 6\r\n" );
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document.write( "       Add those two equations:\r\n" );
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document.write( "                    7a - 8b      = 26\r\n" );
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document.write( "      \r\n" );
document.write( "This gives you two equations in two unknowns.\r\n" );
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document.write( "                         4a -  b = 23 \r\n" );
document.write( "                         7a - 8b = 26\r\n" );
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document.write( "Solve for those two unknowns.\r\n" );
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document.write( "       Multiply the first equation thru by -8 so the b's will cancel:\r\n" );
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document.write( "                        -32a + 8b = -184\r\n" );
document.write( "                          7a - 8b =   26\r\n" );
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document.write( "       Add those two equations\r\n" );
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document.write( "                        -25a      = -158  \r\n" );
document.write( "                           a      = 158/25 = 6.32\r\n" );
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document.write( "       Substitute 6.32 for a in 4a - b = 23\r\n" );
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document.write( "                           4a - b = 23\r\n" );
document.write( "                      4(6.32) - b = 23\r\n" );
document.write( "                        25.28 - b = 23\r\n" );
document.write( "                               -b = -2.28\r\n" );
document.write( "                                b = 2.28       \r\n" );
document.write( "         \r\n" );
document.write( "Substitute these values in any one of the original equations and solve\r\n" );
document.write( "    for the third unknown. \r\n" );
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document.write( "      Substitute 6.32 for a and 2.28 for b in the first original equation\r\n" );
document.write( "      and solve for c:\r\n" );
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document.write( "                       a - 3b - c = 10 \r\n" );
document.write( "               6.32 - 3(2.28) - c = 10\r\n" );
document.write( "                 6.32 - 6.84  - c = 10\r\n" );
document.write( "                         -.52 - c = 10\r\n" );
document.write( "                               -c = 10.52\r\n" );
document.write( "                                c = 10.52\r\n" );
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document.write( "Solution:   (a, b, c) = (6.32, 2.28, -10.52)  \r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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