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

Algebra ->  Inequalities -> 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      Log On


   

Question 1044082: Hello,
I need help with the following math problem:
"Given that +-3%3C=7x%2B2y%3C=3+ and +-4%3C=y-x%3C=4+, what is the maximum possible value of +x%2By+?"
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) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the lines,
7x%2B2y=3
7x%2B2y=-3
y-x=4
y-x=-4
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,
x%2By=-0.556%2B3.444=2.888
.
.
.
.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply all sides of +-3%3C=7x%2B2y%3C=3+ by 2/9. This would give
+-2%2F3%3C=14x%2F9%2B4y%2F9%3C=2%2F3+ <----Inequality A
Now multiply all sides of +-4%3C=y-x%3C=4+ by 5/9. This would give
+-20%2F9+%3C=+5y%2F9-5x%2F9+%3C=+20%2F9+. <-------Inequality B
Adding the corresponding sides of inequalities A and B, we get
+-2%2F3+-20%2F9+%3C=+14x%2F9%2B4y%2F9+%2B+5y%2F9-5x%2F9+%3C=+2%2F3+%2B20%2F9, or
-26%2F9+%3C=+x%2By+%3C=+26%2F9.
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) About Me  (Show Source):
You can put this solution on YOUR website!
why multiply 4/9 and 5/9?