One Solution, No Solution, Infinite Solutions

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 if a system of equations has one solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means there are no values for the variables that can satisfy all equations in the system, indicating that the lines represented by the equations are parallel.

Front

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

Back

It means there are countless sets of values for the variables that satisfy all equations in the system, indicating that the equations represent the same line.

Front

How can you determine if a system of equations has one solution?

Back

If the equations represent lines that intersect at a single point, the system has one solution.

Front

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

Back

If the equations represent parallel lines that never intersect, the system has no solution.

Front

How can you determine if a system of equations has infinite solutions?

Back

If the equations represent the same line, the system has infinite solutions.

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 do not intersect.

Front

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

Back

Two lines that lie on top of each other.