Question

Consider this system of inequalities.

x + y ≤ –3

y < StartFraction x Over 2 EndFraction

Which graph shows the solution for this system?

Answer 1

Given :    x + y ≤ –3

y  <  x/2

To Find :  graph

Solution:

x + y ≤ –3

Draw line x + y = 3  

taking point ( 0 , -3)  , (-3 , 0)

Check origin

( 0 , 0)

0 + 0 ≤ –3

Does not satisfy

Hence shade all the region opposite side in which origin lies including line

y  <  x/2

2y  < x

Draw  line x  = 2y

check

1 , 1

2 <  1

Does not satisfy

Hence shade  all the region opposite side in which (1,1) lies excluding line

Common area of both is solution :

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