Question 172825
solving by elimination is simply adding or subtracting one equation from another
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with the intention of eliminating one of the variables.
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so lets line the equations up one under the other to have a better look at each variable.
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 x+7y=30....eq 1
9x+6y=99....eq 2
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ok as you observe these equations we try to do the least amount of manipulation as possible to reach our goal.....we can either multiply eq 1 by -9 and add the equations together thus eliminating the x terms, or we could multiply eq 1 by - and eq 2 by -7 and add the two equations togethr to eliminate the y terms.  I choose the first choice
:so -9(x+7y=30) equals -9x-63y=-270..so that is our revised eq 1. lets line them up again.
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-9x-63y=-270
 9x+ 6y=99
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so you see how if we add these two equations together that the x terms are eliminated because -9x+9x=0.  We are left with -63y+6y=-270+99--->
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-57y=-171...dividing by -57 gives us
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{{{highlight(y=3)}}}.
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now we take y's value and plug it back into either original equation to solve for x I choose eq 1
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x+7(3)=30
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x+21=30
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{{{highlight(x=9)}}}
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