Question

If asked to examine the consistencyof the equations should we find the solution or verification alone is enough?

Answer 1

One can find that the system of equations is inconistent without finding a solution. In fact an inconsistent system has no solution. In general, when using elimination method for solving the equations, we will ultimately arrive at an absurd equality like a = b where a and b are different numbers. This will prove that the system is inconsistent. To prove it is consistent however, we will have to find the solution.