One Solution, No Solution, Infinite Solutions

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent lines that intersect at exactly one point.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

Example of a system with no solution: 9y + 8 = 9y - 8. What is the solution?

Back

No Solution.

Front

Example of a system with infinite solutions: -10y - 6 = -10y - 6. What is the solution?

Back

Infinite Solutions.

Front

Example of a system with one solution: 6m + 18 = 2m + 18. What is the solution?

Back

One Solution.

Front

Example of a system with no solution: 2m + 6 = 2m + 12. What is the solution?

Back

No Solution.

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 overlapping lines that are the same.