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': 2x + 3 = 2x + 5. What is the solution?

Back

No Solution.

Front

Example of a system with 'One Solution': 3x + 2 = 5. What is the solution?

Back

x = 1.

Front

Example of a system with 'Infinite Solutions': 4x - 2 = 2(2x - 1). What is the solution?

Back

Infinite Solutions.

Front

How can you identify a system of equations with 'No Solution'?

Back

If simplifying leads to a false statement, like 0 = 5.

Front

How can you identify a system of equations with 'One Solution'?

Back

If simplifying leads to a true statement with a unique value for the variable.

Front

How can you identify a system of equations with 'Infinite Solutions'?

Back

If simplifying leads to a true statement that is always true, like 0 = 0.

Front

What is the graphical representation of 'No Solution'?

Back

Two parallel lines that do not intersect.