SOLUTION: Given that -3 <= 7x + 2y <= 3$ and -4 <= y - x <= 4, what is the maximum possible value of x + y?

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Question 1016784: Given that -3 <= 7x + 2y <= 3$ and -4 <= y - x <= 4, what is the maximum possible value of x + y?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the first inequality by 2/3, and the second inequality by 5/3.
%282%2F3%29%2A-3+%3C=+%2814%2F3%29%2Ax%2B%284%2F3%29%2Ay+%3C=%282%2F3%29%2A3
==> -2+%3C=%2814%2F3%29%2Ax%2B%284%2F3%29%2Ay++%3C=2 <--(A)

%285%2F3%29%2A-4+%3C=+%285%2F3%29%2Ay-%285%2F3%29%2Ax+%3C=%285%2F3%29%2A4
==>-20%2F3+%3C=%285%2F3%29%2Ay-%285%2F3%29%2Ax++%3C=20%2F3 <--(B)
Add inequalities A and B:, to get
-26%2F3+%3C=+3y+%2B+3x++%3C=26%2F3
Divide both sides by 3, to get -26%2F9+%3C=+y+%2B+x++%3C=26%2F9
Therefore the maximum value of x+y is 26/9