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

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
:
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
:
**************************
x + y = -5/9 + 31/9 = 26/9
**************************
:
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.
RELATED QUESTIONS
Given that -3 <= 7x + 2y <= 3$ and -4 <= y - x <= 4, what is the maximum possible value... (answered by robertb)
Given that $-3 \le 7x + 2y \le 3$ and $-4 \le y - x \le 4$, what is the maximum possible... (answered by Alan3354)
HELPPP!!!! DUE TOMORROW!!: Given that $-3 \le 7x + 2y \le 3$ and $-4 \le y - x \le 4$,... (answered by richwmiller,ikleyn,MathTherapy,madyl,greenestamps)
Hello, I need help with the following math problem: "Given that {{{ -3<=7x+2y<=3... (answered by Fombitz,robertb,advanced_Learner)
Given that x * y = 4x-2y find the value of (2 * 3) *... (answered by Alan3354,greenestamps)
If x+y=5 and x and y are positive integers, what is the maximum possible value of x-y?... (answered by ikleyn)
What is the value of this expression when x =4 and y= -3 x^3+y^2+x^2y^3-... (answered by algebrahouse.com)
Given that -4 ≤ x ≤ -2 and 2 ≤ y ≤ 4, what is the largest possible value of... (answered by ikleyn,greenestamps)
If x and y are positive integers such that x=8, what is the maximum possible value of... (answered by Alan3354)