# Consistent and Dependent Systems

The two equations $y=2x+5$ and $y=4x+3$ , 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
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independent
*
.

If a
*
consistent
*
system has an infinite number of solutions, it is
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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.