Given that $-3 \le 7x + 2y \le 3$ and $-4 \le y - x \le 4$, what is the maximum possible value of $x + y$?
Look at the graph here....
https://www.desmos.com/calculator/ylop9twasi
x + y is maximized at the corner point (-5/9, 31/9)
So ..... the max sum is just 26/9
