How many solutions (systems)

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 equations represent parallel lines that never intersect.

Front

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

Back

It means 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 equations represent the same line, so they intersect at every point on that line.

Front

How can you determine if two lines are parallel?

Back

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

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the steepness of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

If two lines have different slopes, what can be said about their intersection?

Back

They will intersect at exactly one point.

Front

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

Back

Two parallel lines that never meet.

Front

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

Back

Two lines that intersect at a single point.