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 no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What does the graph of intersecting lines represent?

Back

It represents a system of equations with a unique solution.

Front

How do you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by algebraic manipulation.

Front

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

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system with infinite solutions?

Back

Two lines that lie on top of each other.