Question

What is the Cramer’s Rule?

Answer

If in the equations. As
$a_{1}x+b_{1}y+c_{1}z=d_1$
$a_{2}x+b_{2}y+c_{2}z=d_2$
$a_{3}x+b_{3}y+c_{3}z=d_3$
$\mathrm{Let}$$D=\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|\ne 0$
$D_1=\left|\begin{array}{ccc}{d}_1& b_1& c_1\\ d_2& b_2& c_2\\ d_3& b_3& c_3\end{array}\right|$
$D_2=\left|\begin{array}{ccc}{a}_1& d_1& c_1\\ a_2& d_2& c_2\\ a_3& d_3& c_3\end{array}\right|$
$D_3=\left|\begin{array}{ccc}{a}_1& b_1& d_1\\ a_2& b_2& d_2\\ a_3& b_3& d_3\end{array}\right|$
$\text{then x}=\frac{D_1}{D}\mathrm{,\; y}=\frac{D_2}{D}\mathrm{,\; z}=\frac{D_3}{D}$

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