Tenemos que
[tex]\det \left( X \right) = \left| {\begin{array}{*{20}c} 8 & { - 5} \\ {25} & 8 \\ \end{array} } \right| = 8 \cdot 8 - 25 \cdot \left( { - 5} \right) = 189 [/tex]
[tex]\det \left( Y \right) = \left| {\begin{array}{*{20}c} 1 & 8 \\ { - 7} & {25} \\ \end{array} } \right| = 25 \cdot 1 - 8 \cdot \left( { - 7} \right) = 81 [/tex]
[tex]\det \left( P \right) = \left| {\begin{array}{*{20}c} 1 & { - 5} \\ { - 7} & 8 \\ \end{array} } \right| = 8 \cdot 1 - \left( { - 7} \right)\left( { - 5} \right) = - 27[/tex]
Entonces, por regla de crámer:
[tex]x = \dfrac{{\det \left( X \right)}} {{\det \left( P \right)}} = \dfrac{{189}} {{ - 27}} = - 7[/tex]
[tex]y = \dfrac{{\det \left( Y \right)}} {{\det \left( P \right)}} = \dfrac{{81}} {{ - 27}} = - 3 [/tex]
