Writing a system as Ax = b lets you solve it as x = A⁻¹b - but numerical software almost never computes the inverse. Why is the formula that makes the theory clear the wrong way to compute the answer?

B. Because forming A⁻¹ does more work and adds more rounding error.

The formula says what the solution is and is not an instruction for finding it: computing A⁻¹ means solving n systems, one per column of the identity, where elimination solves the one you care about, roughly n³ against n³/3. Cramer's rule is another exact formula that is catastrophic to compute with. The clean expression and the good algorithm answer different questions.