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The elimination method is subtracting the two linear equations, to solve for a single variable.
Step 1: find a common coefficient. In this case, we already have a common coefficient. Notice that we have two positive x's. This is exactly what we want, so when we subtract the two equations, it will simply leave us with y. So let's subtract the two equations
x+y=2

xy=14
xx=0
y(y)=2y
214=16
Thus we see
2y=16 (divide by 2 from both sides)
y=8
Step 2: Solve for x
Substitute y=8 into the first equation to find x
x+y=2
x8=2 (add 8 to both sides)
x=6
Step 3: Check your work.
68=2 check!
6(8)=14 check!
Thus our order pair is (6,8).
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Sep 13th, 2015
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