SOLUTION: 1) x ≤ 3y, x≥y. (2) y ≥ 2x, −2x+3y ≤6. (3) 3x +5y ≥ 45, x ≥ 0,y ≥ 0. Solve graphically

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Question 1120284: 1) x ≤ 3y, x≥y. (2) y ≥ 2x, −2x+3y ≤6. (3) 3x +5y ≥ 45, x ≥ 0,y ≥ 0.
Solve graphically
Found 2 solutions by Shin123, ikleyn:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
1)


2)


3) Every point in the shaded area is a solution.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

In my yesterday's posts I explained to you in  VERY  DETAILED  form how to solve such problems.

Therefore,  today I will not go in details and will show you the dry results only.


1) x <= 3y, x >= y. 


Rewrite it in the equivalent form

   y >= ,
   y <= x.





Plot y =  (red)  and  y = x (green)



The set of solutions to the given inequality system are the points in quadrant QI belonging to the angle between 
the red and the green straight rays.


It includes the interior of this angle and the restricting rays.


(2) y >= 2x, -2x+3y <= 6. 

Rewrite it in the equivalent form

   y >= 2x,
   y <= .





Plot y = 2x (red)  and  y =  (green)



The set of solutions to the given inequality system are the points above the red line and below the green line in quadrants 
QI, QII and QIII belonging to the angle between the red and the green straight rays.


It includes the interior of this angle and the restricting rays.


(3) 3x +5y >= 45, x >= 0, y>= 0. 

Rewrite it in the equivalent form

   y >= ,
   x >= 0,  y >=0.





Plot y = 



The set of solutions to the given inequality system are the points above the red line in QI, including the points on this line and on coordinate axes.

--------------

In principle,  I do not like to repeat my explanations again and again to the same person.

Why I do it now in this post is only because I can not see and tolerate this  RUBBISH  that @shin produces
in his posts related to this subject.

Simply ignore it,  for your safety . . .



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