Question

the solution space of inequalities 2x+y <=10
and x‐y<=5 is
(i) includes origin
(ii)incl. (4,3)
which one is correct ​

Answer 1

Given : inequalities 2x+y ≤ 10

and x‐y ≤ 5 is  

To Find :  Correct option

(i) includes origin

(ii)incl. (4,3)

Solution:

2x+y ≤ 10

2(0) + 0 ≤ 10   Hence ( 0 , 0) satisfies 2x+y ≤ 10

2(4) + 3  =  11  ≥ 10  Hence ( 4 ,3 ) does not satisfy 2x+y ≤ 10

x‐y ≤ 5

0 - 0   ≤ 5   Hence ( 0 , 0) satisfies x‐y ≤ 5

4 - 3   ≤ 5  Hence ( 4 , 3) satisfies x‐y ≤ 5

( 0 , 0) satisfy both inequalities

Hence  solution space of inequalities  2x+y ≤ 10 and x‐y ≤ 5 is    includes origin

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