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Infinite Number of Solutions for a System of Linear Equations

Explanation

Infinite Number of Solutions

For a system to have infinitely many solutions, it must mean that the lines intersect at infinitely many points. In fact, it means the lines lie on top of each other.

Infinite number of solutions linear system of equations.svg

Such lines are said to be coincidental, and, as they have the same slope and -intercept, they are different versions of the same line. One example of a system that has an infinite number of solutions is