Number of Solutions (& Basic Systems) Exit Ticket 12/3

Front

What is a solution to a system of linear equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

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 infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

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

Back

If the lines intersect at exactly one point, the system has one solution.

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 infinitely many solutions?

Back

Two overlapping lines that are the same.

Front

What is the slope of a line?

Back

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

Front

What is a y-intercept?

Back

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

Front

What does it mean for two lines to have the same slope?

Back

It means they are parallel and will never intersect unless they are the same line.

Front

What is the difference between consistent and inconsistent systems?

Back

Consistent systems have at least one solution, while inconsistent systems have no solutions.