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 1083513: Given that -3 <= 7x + 2y <= 3 and -4 <= y - x <= 4$, what is the maximum possible value of x + y?
Found 2 solutions by rothauserc, KMST:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) 7x + 2y = 3
:
2) y - x = 4
:
solve equation 2 for y
:
y = x + 4
:
substitute for y in equation 1
:
7x + 2(x + 4) = 3
7x + 2x + 8 = 3
9x = -5
x = -5/9
y = -5/9 + 4 = -5/9 + 36/9 = 31/9
:
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x + y = -5/9 + 31/9 = 26/9
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:

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The solution to each (compound) inequality can be graphed as
2 parallel lines, and all the (x,y) points in between.
The solution to the whole system is a parallelogram including its sides.
Point (0,0) is included in the parallelogram.
The lines x+y=constant are parallel to each other,
but not parallel to any side of the parallelogram,
So, one of them will just touch one vertex.
The sum x+y at that point is the maximum.

That vertex must be the intersection of boundary lines
7x%2B2y=3 and y=x%2B4 <---> y-x=4.
Substituting, we get
7x%2B2%28x%2B4%29=3
7x%2B2x%2B8=3
9x=-5
x=-5%2F9
Then,y=-5%2F9%2B4=31%2F9 , and
x%2By=-5%2F9%2B31%2F9=26%2F9=2%268%2F9
Just graph the lines, and check my calculations.