One Solution, No Solution, Infinite Solutions

A set of two or more equations with the same variables.

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

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

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

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

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

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

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

The system has no solution because the lines are parallel.

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