Question 1016784
Multiply the first inequality by 2/3, and the second inequality by 5/3.

{{{(2/3)*-3 <= (14/3)*x+(4/3)*y <=(2/3)*3}}}
==> {{{-2 <=(14/3)*x+(4/3)*y  <=2}}} <--(A)


{{{(5/3)*-4 <= (5/3)*y-(5/3)*x <=(5/3)*4}}}
==>{{{-20/3 <=(5/3)*y-(5/3)*x  <=20/3}}} <--(B)

Add inequalities A and B:, to get

{{{-26/3 <= 3y + 3x  <=26/3}}}
Divide both sides by 3, to get {{{-26/9 <= y + x  <=26/9}}}

Therefore the maximum value of x+y is 26/9