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 has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean if a system has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.

Front

How do you find the solution of a system of equations?

Back

You can use methods like substitution, elimination, or graphing.

Front

What is the substitution method?

Back

A method where you solve one equation for one variable and substitute it into the other equation.

Front

What is the elimination method?

Back

A method where you add or subtract equations to eliminate one variable.

Front

What does the graph of a system with one solution look like?

Back

Two lines that intersect at a single point.

Front

What does the graph of a system with no solution look like?

Back

Two parallel lines that never meet.

Front

What does the graph of a system with infinitely many solutions look like?

Back

Two lines that lie on top of each other.