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

Example of a system with one solution: 2x + 3 = 7 and x - 1 = 1. How many solutions does it have?

Back

One Solution.

Front

Example of a system with no solution: 2x + 3 = 5 and 2x + 3 = 7. How many solutions does it have?

Back

No Solution.

Front

Example of a system with infinite solutions: 3x + 6 = 9 and x + 2 = 3. How many solutions does it have?

Back

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 never meet.

Front

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

Back

Two overlapping lines that are identical.