SOLUTION: Hello, I need help with the following math problem: "Given that {{{ -3<=7x+2y<=3 }}} and {{{ -4<=y-x<=4 }}}, what is the maximum possible value of {{{ x+y }}}?" Please giv

Question 1044082: Hello,
I need help with the following math problem:
"Given that and , what is the maximum possible value of ?"
Please give a detailed explanation of how to solve this problem.
Thank you,
Nicole
Found 3 solutions by Fombitz, robertb, advanced_Learner:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Graph the lines,

Look for the intersection points.
The one with the maximum value will be the one that is most to the right and most above the x-axis.
In this case,

.
.
.
.
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Multiply all sides of by 2/9. This would give
<----Inequality A
Now multiply all sides of by 5/9. This would give
. <-------Inequality B
Adding the corresponding sides of inequalities A and B, we get
, or
.
So from this we could see that the maximum value of x+y is 26/9, while its minimum value is -26/9.

Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
why multiply 4/9 and 5/9?
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