Question 177969
addition is really just another name for elimination
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these two equations are already set up and do not have to be manipulated at all because one of the variables will be eliminated just by adding the equations together.
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x+y=7....eq 1
x-y=9....eq 2
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notice as these are lined up that when we add the two equations together the y terms are eliminated? why? because +y-y=0.  We are left with x+x=7+9
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2x=16
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{{{highlight(x=8)}}}
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now take x's found value of 8 and plug it into either eq 1 or 2 and solve for y. I chose eq 1
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8+y=7
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{{{highlight(y=-1)}}}
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so the solution(8,-1) whould work in both equations
:
x+y=7....eq 1--->8+(-1)=7--->7=7....check
x-y=9....eq 2--->8-(-1)=9--->9=9....check