Solutions to systems of equations

Front

What is a solution to a system of equations?

Back

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

Front

What does it mean if two lines intersect at one point?

Back

It means the system of equations has one unique solution.

Front

What does it mean if two lines are parallel?

Back

It means the system of equations has no solution.

Front

What does it mean if two lines are the same line?

Back

It means the system of equations has infinitely many solutions.

Front

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

Back

If the lines are parallel, they will never intersect.

Front

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

Back

Two lines intersecting at a single point.

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 lines that lie on top of each other.

Front

If a system of equations has infinitely many solutions, what can be said about the equations?

Back

The equations are dependent and represent the same line.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable.