Question 178131
substitution: take one equation and isolate a variable then take the value of the variable and plug it into the OTHER equation
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2x+y=7.....eq 1
x+5y=12....eq 2
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rewrite eq 1 to y=-2x+7....now take the value of y which is -2x+7 and plug that into eq 2 for every y that you see
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x+5(-2x+7)=12
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x-10x+35=12.......distributed left side
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-9x=-23............combined like terms on either side
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{{{highlight(x=23/9)}}}
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now take the found value of x and plug it into either equation to find y
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y=-2x+7--->y=-2(23/9)+7--->-46/9+63/9={{{highlight(17/9)}}}
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Elimination or addition method: This is manipulating one or both of the equations so as to eliminate one of the variables.  It is really important, when learning this method to always line up the terms so as to SEE what is taking place
:.
2x+y=7.....eq 1
x+5y=12....eq 2
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We can either choose to eliminate the x or y terms.  To eliminate the y terms we would multiply eq 1 by -5 and add the equations together or we can eliminate the x terms by multiplying eq 2 by -2 and adding the equations together. I choose to eliminate the x terms
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eq 2----->-2(x+5y=12)---->-2x-10y=-24....now take this and line it up under eq 1
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2x+y=7........eq 1
-2x-10y=-24...eq 2 revised
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now you can clearly see if you add the terms of each equation together that the x terms are eliminated because 2x-2x=0.  We are left with y-10y=7-24
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-9y=-17
:
{{{highlight(y=17/9)}}}
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now take y's found value and plug it back into any numbered equation we have.
I choose eq 1
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2x+17/9=7......plugged in y value of 17/9
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18x+17=63......multiplied each term by 9 to get rid of fraction
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18x=46
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{{{highlight(x=46/18=23/9)}}}
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{{{w^5}}}which was what we wanted......
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Mathtut