One Solution, No Solution, Infinite Solutions

Front

What are the three types of solutions for a system of equations?

Back

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

How can you determine if a system of equations has 'No Solution'?

Back

If the equations simplify to a contradiction, such as 0 = 5, then there is no solution.

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 solution for the variable, then there is one solution.

Front

How can you determine if a system of equations has 'Infinite Solutions'?

Back

If the equations simplify to an identity, such as 0 = 0, then there are infinite solutions.

Front

What is an example of a system of equations with 'No Solution'?

Back

y = 2x + 1 and y = 2x - 3 are parallel lines, hence no solution.

Front

What is an example of a system of equations with 'One Solution'?

Back

y = 2x + 1 and y = -x + 3 intersect at one point, hence one solution.

Front

What is an example of a system of equations with 'Infinite Solutions'?

Back

2x + 4 = 2(x + 2) represents the same line, hence infinite solutions.