Systems of Equations

Front

What does it mean if a system of linear equations is consistent and independent?

Back

The lines represented by the equations intersect at exactly one point.

Front

What are the characteristics of a consistent and dependent system of equations?

Back

The system has infinitely many solutions, and the lines represented by the equations are the same line.

Front

What does it mean if a system of linear equations is inconsistent?

Back

The system has no solutions, and the lines represented by the equations are parallel.

Front

How many solutions does a consistent and independent system of equations have?

Back

Exactly one solution.

Front

How many solutions does a consistent and dependent system of equations have?

Back

Infinitely many solutions.

Front

How many solutions does an inconsistent system of equations have?

Back

No solutions.

Front

What is the graphical representation of intersecting lines in a system of equations?

Back

The lines cross at a single point, indicating one solution.

Front

What is the graphical representation of parallel lines in a system of equations?

Back

The lines never intersect, indicating no solutions.

Front

What is the graphical representation of the same line in a system of equations?

Back

The lines overlap completely, indicating infinitely many solutions.

Front

What is the definition of a system of equations?

Back

A set of two or more equations with the same variables.