EXAMPLES OF INCONSISTENT SYSTEM OF EQUATIONS
x+2y=3, 2y+x=4 is inconsistent because x+2y is the same as 2y+x. This sum cannot be both 3 and 4.
2a+2b=8, 3a+3b=14 is inconsistent because a+b cannot be equal to both 4 and 14/3.
A clue for consistency is that the number of equations in the system must be equal to the number of unknowns. Too few equations implies many solutions; but too many equations could imply inconsistency. So in the latter case, use only as many equations as there are unknowns, and discard any surplus equations. After solving the system, substitute the solution (the discovered values of the unknowns) into the discarded equations to see if they’re satisfied. If they are not satisfied, the system is inconsistent.