When solving 3 simultaneous linear equations then one of the following geometrical will occur which are represented by the 3 planes.
1) A unique single solution means that all three planes intersect at a point.
2) An infinite number of solutions which would mean that one or more planes may intersect along a line.
3) No solution which would mean that there is no intersection and that the planes are parallel.
In cases 2) and 3) the determinant of the coefficient matrix is zero.
If there is a unique solution or an infinite number of solutions as in cases 1) and 2), we say that the equations are consistent
If there is no solution as in case 3) then we say the equations are inconsistent.
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