document.write( "Question 385212: Can I please get some assistance for this problem? Thank you. \r
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Algebra.Com's Answer #272556 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2x+3y+7z =  13\r\n" );
document.write( "3x+2y-5z = -22\r\n" );
document.write( "5x+7y-3z = -28 \r\n" );
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document.write( "1. Pick a letter to eliminate and two equations that contain that letter.\r\n" );
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document.write( "I will arbitrarily pick the letter y to eliminate and I will arbitrarily\r\n" );
document.write( "pick the equations:\r\n" );
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document.write( "3x+2y-5z = -22\r\n" );
document.write( "5x+7y-3z = -28\r\n" );
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document.write( "to eliminate y from.\r\n" );
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document.write( "Since the coefficients of y are 2 and 7, multiply the first\r\n" );
document.write( "equation through by -7 and the second one through by 2 so\r\n" );
document.write( "they will have coefficients that will cancel when equals are\r\n" );
document.write( "added to equals:\r\n" );
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document.write( "-21x-14y+35z = 154\r\n" );
document.write( " 10x+14y- 6z = -56\r\n" );
document.write( "-------------------\r\n" );
document.write( "-11x    +29z =  98\r\n" );
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document.write( "2. Next, eliminate that same letter from one of those equation\r\n" );
document.write( "   and the equation you did not use in step 1.\r\n" );
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document.write( "I did not use \r\n" );
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document.write( "2x+3y+7z =  13\r\n" );
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document.write( "in step 1. I will use it with\r\n" );
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document.write( "3x+2y-5z = -22\r\n" );
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document.write( "to eliminate the same letter y.\r\n" );
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document.write( "3x+2y-5z = -22\r\n" );
document.write( "2x+3y+7z =  13\r\n" );
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document.write( "Multiply the first one through by -3 and the second\r\n" );
document.write( "one through by 2:\r\n" );
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document.write( "-9x-6y+15z = 66\r\n" );
document.write( " 4x+6y+14z = 26\r\n" );
document.write( "---------------\r\n" );
document.write( "-5x   +29z = 92\r\n" );
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document.write( "3.  Now you have a system of only two equations in two letters:\r\n" );
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document.write( "-11x+29z = 98\r\n" );
document.write( " -5x+29z = 92\r\n" );
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document.write( "Multiply the first equation through by -1\r\n" );
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document.write( " 11x-29z = -98\r\n" );
document.write( " -5x+29z =  92\r\n" );
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document.write( "  6x     =  -6\r\n" );
document.write( "       x = -1\r\n" );
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document.write( "4. Now we switch over to substitution.  Substitute what you\r\n" );
document.write( "got in step 3 in one of those last two equations in only two \r\n" );
document.write( "letters.\r\n" );
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document.write( "I will substitute -1 for x in one of those last two equations in\r\n" );
document.write( "only two letters:\r\n" );
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document.write( "I will pick this one:\r\n" );
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document.write( "   -5x+29z = 92\r\n" );
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document.write( "-5(-1)+29z = 92 \r\n" );
document.write( "     5+29z = 92\r\n" );
document.write( "       29z = 87\r\n" );
document.write( "         z = 3\r\n" );
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document.write( "5. Substitute those two letters in one of the original equations\r\n" );
document.write( "that contains the first letter you eliminated.\r\n" );
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document.write( "I will substitute -1 for x and 3 for z in this original equation: \r\n" );
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document.write( "     3x+2y-5z = -22\r\n" );
document.write( "3(-1)+2y-5(3) = -22\r\n" );
document.write( "     -3+2y-15 = -22\r\n" );
document.write( "        2y-18 = -22\r\n" );
document.write( "           2y = -4\r\n" );
document.write( "            y = -2\r\n" );
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document.write( "The solution is (x,y,z) = (-1,-2,3).\r\n" );
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document.write( "Edwin
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