Which system of inequalities has no solution? a. x+3y is greater than or equal to 0.5 x+3y is less than or equal to 2.5 b. x+3y is greater than or equal to 0.5 x+3y is greater than or equal to 2.5 c. x+3y is less than or equal to 0.5 x+3y is greater than or equal to 2.5

The answer is C. Just took the test

The system of inequalities has no solution is:

              Option: C

x+3y is less than or equal to 0.5

x+3y is greater than or equal to 2.5

A.

x+3y is greater than or equal to 0.5  i.e. x+3y ≥ 0.5

x+3y is less than or equal to 2.5 i.e. x+3y ≤ 2.5

Hence, the common region i.e. obtained from the above 2 inequalities is:

        0.5 ≤ x+3y ≤ 2.5

B.

x+3y is greater than or equal to 0.5  i.e. x+3y ≥ 0.5

x+3y is greater than or equal to 2.5 i.e. x+3y ≥ 2.5

Hence, the common region of the two inequalities will be:

                  x+3y ≥ 2.5

C.

x+3y is less than or equal to 0.5  i.e.  x+3y ≤ 0.5

x+3y is greater than or equal to 2.5 x+3y ≥ 2.5

Hence, the intersection of the region obtained by two inequalities will be empty set.

Hence, the system of inequalities is empty.

Also, by the graph attached of option: C. , it could be observed.