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)   (Show Source):
You can put this solution on YOUR website! 1) 7x + 2y = 3
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2) y - x = 4
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solve equation 2 for y
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y = x + 4
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substitute for y in equation 1
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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)  (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
 and  <--->  .
Substituting, we get
Then, , and
Just graph the lines, and check my calculations.
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