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 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 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 they intersect at every point on that line.

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

Back

x = 3.

Front

Example of a system with infinite solutions: 3x + 6 = 3(x + 2). What is the solution?

Back

Infinite Solutions.

Front

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

Back

If the equations simplify to a false statement, like 0 = 5.

Front

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

Back

If the equations simplify to a true statement with a unique value for the variable.

Front

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

Back

If the equations simplify to a true statement that is always true, like 0 = 0.