System of Equations

Two equations together are called a system of equations. A solution of a system of equations is an ordered pair of numbers that satisfies both equations. A system of two linear equation can have 0, 1 or an infinite number of solutions.

A system of equations is consistent if there is at least one ordered pair that satisfies both equations. If there is only one solution, the system is independent. If there are infinite solutions, the system is dependent.

If the graphs of two linear equations coincide, there are an infinite number of solutions.

If the graphs are parallel,  there are no solutions, and the system is inconsistent.