Types of Solutions to System of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means the lines represented by the equations overlap completely, representing the same line.

Front

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

Back

Two parallel lines.

Front

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

Back

Two intersecting lines.

Front

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

Back

Overlapping lines.

Front

How can you determine if two equations have the same slope?

Back

By comparing the coefficients of the x terms in the equations.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = 3x - 5?

Back

The y-intercept is -5.