Systems Of Equations #of Solutions

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines represented by the equations coincide, or are the same line.

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

How can you determine if a system of equations has one solution?

Back

If the slopes of the lines are different, the system has one solution.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

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

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

The system has no solution because the lines are parallel.

Front

If two lines have the same slope and the same y-intercept, what can be said about their solutions?

Back

The system has infinitely many solutions because the lines coincide.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane.