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.

Front

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

Back

It means the equations intersect at exactly one point, representing a unique solution.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line, so there are countless points of intersection.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the equations to see if they intersect, are parallel, or are identical.

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

Example of a system with no solution: 5y + 10 = 5y + 20. What is the solution?

Back

No Solution.

Front

Example of a system with one solution: -5y - 15 = 5y - 10. What is the solution?

Back

One Solution.

Front

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

Back

Two overlapping lines on a graph.