Question

Is the statement "Two equivalent linear systems can have different solution sets" true or false? Explain.

A. True. Equivalent systems may have different solutions.
B. False. Equivalent systems always have the same solution set.
C. True. Equivalent systems cannot have different solution sets.
D. False. Equivalent systems are inconsistent.

Answer 1

The statement is false. Two equivalent linear systems will always have the same solution set because they represent the same geometric relationships.

Step-by-step explanation:

The statement "Two equivalent linear systems can have different solution sets" is false. Equivalent linear systems always have the same solution set. When we say two systems are equivalent, it means that every solution of one system is a solution of the other, and vice versa.

This relationship is due to the fact that equivalent systems represent the same geometric figure, typically lines that coincide, intersect at a single point, or are parallel with no points of intersection, resulting in a single solution, infinitely many solutions, or no solution respectively.