document.write( "Question 267018: Solve By The Addition Method ?\r
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Algebra.Com's Answer #196053 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Pick a letter and pick two equations to \r\n" );
document.write( "eliminate it from:\r\n" );
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document.write( "I'll pick z and the first and second equations\r\n" );
document.write( "to eliminate it from:\r\n" );
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document.write( "Just add them term by term as they are and the\r\n" );
document.write( "z's will cancel out.\r\n" );
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document.write( "Now pick another pair (you have to use one of the\r\n" );
document.write( "same equations you used before, but make sure\r\n" );
document.write( "that you use the third one, the one you \r\n" );
document.write( "haven't used) and eliminate the SAME letter from\r\n" );
document.write( "them.\r\n" );
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document.write( "I'll pick the second and third:\r\n" );
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document.write( "Just add them term by term as they are and the\r\n" );
document.write( "z's will also cancel out.\r\n" );
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document.write( "That equation can be divided through by 2, so we\r\n" );
document.write( "will go ahead and do that, since it will be\r\n" );
document.write( "simpler.\r\n" );
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document.write( "So now we have reduced it from three equations in three\r\n" );
document.write( "variables, to just two equations in two variables:\r\n" );
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document.write( "We will eliminate the y's by multiplying the first equation\r\n" );
document.write( "through by -3\r\n" );
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document.write( "Add them term by term and get:\r\n" );
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document.write( "Divide both sides by -7\r\n" );
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document.write( "Since that is a terrible fraction, we won't substitute,\r\n" );
document.write( "but instead go back to \r\n" );
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document.write( "and eliminate the x's instead:\r\n" );
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document.write( "3x and 2x can both be made into 6x, and so they will\r\n" );
document.write( "cancel, we multiply the first equation through by 2\r\n" );
document.write( "and the second ione through by -3 and we get\r\n" );
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document.write( "Add them term by term and get:\r\n" );
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document.write( "Divide both sides by 7\r\n" );
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document.write( "That's also a terrible fraction, we could start\r\n" );
document.write( "all over and eliminate another variable, but\r\n" );
document.write( "that would just take too long.  So instead we'll just\r\n" );
document.write( "suffer through substituting the two terrible \r\n" );
document.write( "fractions for x and y into one of the original\r\n" );
document.write( "equations.\r\n" );
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document.write( "We can clear of fractions by multiplying through\r\n" );
document.write( "by 7:\r\n" );
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document.write( "Divide both sides by 21\r\n" );
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document.write( "My! What terrible fractions those answers are!\r\n" );
document.write( "But sometimes that's the case.  And those\r\n" );
document.write( "answers are correct, if you copied the problem\r\n" );
document.write( "correctly, as\r\n" );
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document.write( "So (x,y,z) = (,,)\r\n" );
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document.write( "Edwin
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