Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting it into the other.

Front

How do you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

How do you determine if two lines are intersecting?

Back

If they have different slopes.

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.