Question

How will the solution of the system y > 2x and y < 2x change if the inequality sign on both inequalities is reversed?

a. No change
b. The solution set will be empty.
c. The solution set will include all real numbers.
d. The solution set will be a single point.

Answer 1

If we reverse the inequality signs in the system y > 2x and y < 2x, the solution set will be empty.

Step-by-step explanation:

If we reverse the inequality signs in the system y > 2x and y < 2x, the solution set will be empty. This means that there will be no values of x and y that satisfy both conditions. When we reverse the inequality signs, we are essentially changing the direction of the inequality symbols, which alters the relationship between x and y in the system. In this case, reversing the signs creates an inconsistent and contradictory system, resulting in an empty solution set.