document.write( "Question 35855: Solve the linear system...if the system is inconsistent or dependent, so state:\r
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Algebra.Com's Answer #21946 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
3x + 2y +  z =   2\r\n" );
document.write( "4x -  y + 3z = -16\r\n" );
document.write( " x + 3y -  z =  12\r\n" );
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document.write( "1. If there is an equation with only two unknowns in it, then use it, and\r\n" );
document.write( "skip to step 3.  Otherwise, create an equation in only two unknowns by using\r\n" );
document.write( "step 2.\r\n" );
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document.write( "There is no equation in only two unknowns, so we must go to step 2\r\n" );
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document.write( "2. Arbitrarily pick two equations, and an unknown to eliminate from them.\r\n" );
document.write( "Although it really doesn't matter which two equations you pick, you will\r\n" );
document.write( "save time by picking two equations which have an unknown easy to eliminate.\r\n" );
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document.write( "I will arbitrarily pick the first and third, and unknown z to eliminate,\r\n" );
document.write( "because I can just add them as they are and the z's will cancel  \r\n" );
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document.write( "3x + 2y + z =  2\r\n" );
document.write( " x + 3y - z = 12\r\n" );
document.write( "覧覧覧覧覧覧覧覧\r\n" );
document.write( "4x + 5y     = 14\r\n" );
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document.write( "3. Pick a pair of equations (not the same pair you picked in step 2 (if you did\r\n" );
document.write( "step 2), and eliminate from them the SAME unknown which is missing in your\r\n" );
document.write( "equation in only two unknowns you got from either step 1 or 2.\r\n" );
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document.write( "I will pick the 2nd and 3rd equations, and I have no choice but to eliminate\r\n" );
document.write( "z from them, bacause that is the unknown that is missing in the equation I \r\n" );
document.write( "got from step 2. \r\n" );
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document.write( "4x -  y + 3z = -16\r\n" );
document.write( " x + 3y -  z =  12\r\n" );
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document.write( "To eliminate z, multiply the second equation by 3 and add to the first\r\n" );
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document.write( "4x -  y + 3z = -16\r\n" );
document.write( "3x + 9y - 3z =  36\r\n" );
document.write( "覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "7x + 8y      =  20\r\n" );
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document.write( "4. Solve the pair of equations in two unknowns for the unknowns.\r\n" );
document.write( "You may use either substitution of addition-subtraction/elimination\r\n" );
document.write( "method:\r\n" );
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document.write( "Solve the system by whatever method you like best. If you can't solve\r\n" );
document.write( "a system of two equations in two unknowns, then post again.  Assuming\r\n" );
document.write( "you know how to solve this system:\r\n" );
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document.write( "4x + 5y = 14\r\n" );
document.write( "7x + 8y = 20  \r\n" );
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document.write( "I'll just give you this answer:  you get x = -4 and y = 6\r\n" );
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document.write( "5.  From the original system, arbitrarily pick an equation that contains the\r\n" );
document.write( "other unknown you still don't have the value of.  Substitute the values for\r\n" );
document.write( "the two unknowns you now have and solve for the final letter.\r\n" );
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document.write( "I arbitrarily pick the first original equation\r\n" );
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document.write( "3x + 2y + z = 2 and replace x by -4 and y by 6\r\n" );
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document.write( "3(-4) + 2(6) + z = 2\r\n" );
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document.write( "-12 + 12 + z = 2\r\n" );
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document.write( "           z = 2\r\n" );
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document.write( "So the final solution is (x, y, z) = (-4, 6, 2)\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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