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Suppose we have two linear equations in two unknowns. If the equations are plotted on a rectangular grid, the graph will fit one of these scenarios: 1) The two lines cross each other (intersect). 2) The two lines don't cross - they are parallel lines 3) The two lines fall on top of each other - they're really the same line. In case 3) the two lines are dependent - one can be changed into the other. In cases 1) and 2) we say the lines are independent. If the pair of equations has a solution (one or more points in common) we say they are consistent ... cases 1) and 3). In case 2) the system is inconsistent; there is no solution. To summarize: 1) Intersecting lines are consistent and independent. 2) Parallel lines are inconsistent and independent. 3) Coincident ["happen together"] lines are consistent and dependent. *** A second order linear system CANNOT be both dependent and inconsistent.
-1 to the 7th power equals -1