In this [article](https://www.purplemath.com/modules/cramers.htm) (near the end), they say that we can not apply Cramer's rule to find our unknowns if the determinant is 0.

In this [stack](https://math.stackexchange.com/questions/640554/set-of-linear-equation-has-no-solution-or-unique-solution-or-infinite-solution?noredirect=1&lq=1), I saw an answer which tries to explain using Cramer's rule but I don't think it's very clear. I am looking for a geometric intuition of how to test the nature of the solution using Cramer's rule.