Station 1: Solutions to Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear 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 infinitely many solutions?

Back

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

Front

How can you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

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

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never meet.

Front

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

Back

Two identical lines that lie on top of each other.

Front

What is the solution of a system of linear equations?

Back

The point where the graphs of the equations intersect.

Front

What is the slope of a line?

Back

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