Question

resolver cada sistema de ecuaciones porla regla de cramer

a). {x - 5y =8

      -7x+8y=25

Answer 1

Tenemos que

 

$<var>\det \left( X \right) = \left| {\begin{array}{*{20}c} 8 & { - 5} \\ {25} & 8 \\ \end{array} } \right| = 8 \cdot 8 - 25 \cdot \left( { - 5} \right) = 189 </var>$

 

$<var>\det \left( Y \right) = \left| {\begin{array}{*{20}c} 1 & 8 \\ { - 7} & {25} \\ \end{array} } \right| = 25 \cdot 1 - 8 \cdot \left( { - 7} \right) = 81 </var>$

 

$<var>\det \left( P \right) = \left| {\begin{array}{*{20}c} 1 & { - 5} \\ { - 7} & 8 \\ \end{array} } \right| = 8 \cdot 1 - \left( { - 7} \right)\left( { - 5} \right) = - 27</var>$

 

Entonces, por regla de crámer:

 

$<var>x = \dfrac{{\det \left( X \right)}} {{\det \left( P \right)}} = \dfrac{{189}} {{ - 27}} = - 7</var>$

 

$<var>y = \dfrac{{\det \left( Y \right)}} {{\det \left( P \right)}} = \dfrac{{81}} {{ - 27}} = - 3 </var>$