Question

A system of three linear equations in three variables is consistent and dependent. How many solutions to the system exist?

-none
-one
-three
-infinite

Answer 1

Answer: Infinite Many Solutions.

Explanation:

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Answer 2

Given a system of three linear equations in three variables which is consistent and dependent.

A system is said to be consistent if it has at least one solution. A system which has no solution is said to be inconsistent.

A consistent solution is said to be independent if it has only one solution and is said to be dependent if it has an infinitely many solutions.

Therefore, given a system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.