Question

If a system of linear equations has infinitely many solutions, then the system is called____ . If a system of linear equations has no solution, then the system is called_____.

Short answer

Dependent system, inconsistent system

Step-by-step solution

Step 1. Given information

Two incomplete sentences are given.

Step 2. Concept used

A linear system in three variables determines a collection of planes. The intersection point is the solution.

Step 3. Calculation

So, we know that if a system of linear equations has infinitely many solutions, then the system is called a dependent system.

And we also know that if a system of linear equations has no solution then the system is called an inconsistent system.