Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so they intersect at every point on that line.

Front

How can you determine if a system of equations has no solution?

Back

If the equations are parallel, they will have the same slope but different y-intercepts.

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 lines that lie on top of each other.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

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