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

The equations intersect at exactly one point, meaning there is a unique solution for the variables.

Front

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

Back

The equations represent parallel lines that never intersect, indicating that there is no set of values for the variables that satisfies both equations.

Front

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

Back

The equations represent the same line, meaning any point on the line is a solution.

Front

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

Back

If the equations are parallel (same slope but different y-intercepts), they have no solution.

Front

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

Back

If the equations have different slopes, they will intersect at one point, resulting in one solution.

Front

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

Back

If the equations are equivalent (one can be transformed into the other), they have infinite solutions.

Front

Example of a system with one solution: 2x + 3y = 6 and x - y = 1. What is the solution?

Back

(3, 0) is the solution where the two lines intersect.

Front

Example of a system with no solution: 2x + 3y = 6 and 2x + 3y = 8. What is the conclusion?

Back

The system has no solution because the lines are parallel.

Front

Example of a system with infinite solutions: 2x + 3y = 6 and 4x + 6y = 12. What is the conclusion?

Back

The system has infinite solutions because the second equation is a multiple of the first.