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 for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of equations by elimination?

Back

You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never meet.

Front

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

Back

Two overlapping 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 elimination method?

Back

A method for solving systems of equations by removing one variable.