classifying linear systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean if a linear system has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a linear system has one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean if a linear system has infinitely many solutions?

Back

It means the lines coincide, or are the same line, resulting in an infinite number of intersection points.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How can you determine if two lines are coincident?

Back

Two lines are coincident if they have the same slope and the same y-intercept.

Front

What is the graphical representation of a system with no solution?

Back

The graphical representation shows two parallel lines that never intersect.

Front

What is the graphical representation of a system with one solution?

Back

The graphical representation shows two lines that intersect at a single point.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The graphical representation shows one line on top of another, indicating they are the same line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.