Cramer's rule doesn't work in this case. Why? Here I have these equations,
x + y + z = 2,
2x + 3y + 2z = 5,
2x + 3y + 15z = 5
When solving normally, we get (x,y,z) = (1,1,0) but when used cramer's rule, we get
Delta = 0 , Delta x = 13, Deltta y = 13, Delta z = 0. It means that the given system of equation is inconsistent. How can this be possible?
EDIT : Determinant is not 0, it's 13. I just wrote the terms wrong when calculating :p

$$\Delta=\det\left(
\begin{array}{ccc}
 1 & 1 & 1 \\
 2 & 3 & 2 \\
 2 & 3 & 15 \\
\end{array}
\right)=13$$
and
$$\Delta_x=\det\left(
\begin{array}{ccc}
 2 & 1 & 1 \\
 5 & 3 & 2 \\
 5 & 3 & 15 \\
\end{array}
\right)=13$$
To solve with Cramer's rule you must do
$$x=\frac{\Delta_x}{\Delta}=\frac{13}{13}=1$$
And so on for the other unknowns
