Question

The origin is contained in the solution set for the following system of inequalities:

2x + y < 5
2x - y< 3
Select one:
O True
O False​

Answer 1

The correct option is:

TRUE

Explanation:

We have been given a system of inequalities:

2x + y < 5

2x - y < 3

We want to check if the origin is contained in the solution in this system of inequalities.

Substitute the origin (0,0) in both inequalities.

2(0) +0 < 5

0 < 5

Thus, the inequality holds true

2(0) - 0 < 3

0 < 3

Thus the inequality holds true.

As the origin (0,0) satisfied both of the inequalities, the origin is contained in the solution set of the system of inequalities