Question

Consider the solution to the system of inequalities below.

{y less than or equal to 0.5x +2
{y greater than 3x-3

which of the following functions could be added to the system without changing the solution set?
y > 2
y < 2
y > 3
y = 3

Answer 1

y<2

Explanation:

Answer 2

Answer: y<2

Explanation:

Since we can say a functions could be added to the system without changing the solution set if after including it to the system the feasible region of entire system is not affected.

Here, the solution to the system of inequalities is,

y≤ 0.5x+2

y>3x-3

Since after ploting these two enequslties in the graph we get our feasible region.

When we include y > 2 in the system there is no solution of the system.

Therefore it affects the system.

Now when we include y < 2 in the system the solution or feasible region remain same.

Therefore it does not affect the system.

When we include y > 3 in the system there is no solution of the system.

Therefore it affects the system.

When we include line y=3 in the system then the system has no solution.

Therefore, it affects the system.

Thus, second Option is correct.