You can put this solution on YOUR website! X+Y=1
X=1-Y
(1-Y)+Y=2
1-Y+Y=2
0Y=1 NO SOLUTION
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X+Y=1 & X+Y=2 CANNOT BOTH BE VALID BECAUSE 1 DOES NOT EQUAL 2
PROOF
SET (X+Y)=Z
NOW SOLVE
Z=1 & Z=2
Z CANNOT BE 1 & 2 IN THE SAME SET OF LINEAR EQUATIONS.