# How is a linear system consistent

## Consistent and Dependent Systems

The two equations and , form a system of equations . The ordered pair that is the solution of both equations is the solution of the system.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions.

If a system has at least one solution, it is said to be * consistent * .

If a * consistent * system has exactly one solution, it is * independent * .

If a * consistent * system has an infinite number of solutions, it is * dependent * . When you graph the equations, both equations represent the same line.

If a system has no solution, it is said to be * inconsistent * . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

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