Number of Solutions to Systems 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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

What is the graphical representation of parallel lines?

Back

Lines that never intersect and have the same slope.

Front

How can you determine if two lines are parallel from their equations?

Back

If they have the same slope but different y-intercepts.

Front

What is the significance of the slope in a system of equations?

Back

The slope determines the steepness and direction of the line; it affects whether lines intersect.

Front

What happens to the number of solutions if two lines have the same slope and the same y-intercept?

Back

There are infinitely many solutions because the lines are identical.

Front

What is the relationship between the slopes of intersecting lines?

Back

They have different slopes.

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel, typically in three-dimensional space.