Question Number 184242 by Shrinava last updated on 04/Jan/23
Answered by SEKRET last updated on 04/Jan/23
$$\:\boldsymbol{\mathrm{metod}}\:\boldsymbol{\mathrm{Kramer}} \\ $$$$\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}\right)\:=\:\:\begin{vmatrix}{\mathrm{4}}&{−\mathrm{5}}&{\:\:\mathrm{2}}\\{\mathrm{3}}&{−\mathrm{2}}&{\:\:\:\mathrm{7}}\\{\mathrm{3}}&{\mathrm{10}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{327} \\ $$$$\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}_{\mathrm{1}} \right)=\:\begin{vmatrix}{\mathrm{9}}&{−\mathrm{5}}&{\mathrm{2}}\\{\mathrm{8}}&{−\mathrm{2}}&{\mathrm{7}}\\{\mathrm{17}}&{\mathrm{10}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{1041} \\ $$$$\:\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}_{\mathrm{2}} \right)=\:\begin{vmatrix}{\mathrm{4}}&{\mathrm{9}}&{\mathrm{2}}\\{\mathrm{3}}&{\mathrm{8}}&{\mathrm{7}}\\{\mathrm{3}}&{\mathrm{17}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{243} \\ $$$$\:\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}_{\mathrm{3}} \right)=\:\begin{vmatrix}{\mathrm{4}}&{−\mathrm{5}}&{\mathrm{9}}\\{\mathrm{3}}&{−\mathrm{2}}&{\mathrm{8}}\\{\mathrm{3}}&{\mathrm{10}}&{\mathrm{17}}\end{vmatrix}=\:\mathrm{3} \\ $$$$\:\:\boldsymbol{\mathrm{x}}\:\:=\:\:\:\frac{−\mathrm{1041}}{−\mathrm{327}}\:\:\:=\:\:\:\:\frac{\mathrm{347}}{\mathrm{109}} \\ $$$$\:\:\boldsymbol{\mathrm{y}}\:\:=\:\:\:\frac{−\mathrm{243}}{−\mathrm{327}}\:\:\:=\:\:\:\:\:\:\:\frac{\mathrm{81}}{\mathrm{109}} \\ $$$$\:\:\boldsymbol{\mathrm{z}}\:\:\:=\:\:\:\frac{\mathrm{3}}{−\mathrm{327}}\:\:=\:\:\:\:\:\:\:\:\frac{−\mathrm{1}}{\mathrm{109}} \\ $$