Question

1/x + 1/y = 5

3/x + 2/y = 12

resolver este sistema de ecucaciones

Answer 1

$<var>\left. {\begin{array}{*{20}c} {\dfrac{1} {x} + \dfrac{1} {y}} & = & 5 \\ {\dfrac{3} {x} + \dfrac{2} {y}} & = & {12} \\ \end{array} } \right\}\xrightarrow{{ \cdot xy}}\left. {\begin{array}{*{20}c} {x + y} & = & {5xy} \\ {2x + 3y} & = & {12xy} \\ \end{array} } \right\}</var>$

$<var>\xrightarrow{{ - 3 \cdot Ec1}}\left. {\begin{array}{*{20}c} { - 3x - 3y} & = & { - 15xy} \\ {2x + 3y} & = & {12xy} \\ \end{array} } \right\}\xrightarrow{{Ec.1 + Ec.2}} - x = - 3xy</var>$

 

$<var>\xrightarrow{{:( - 3x)}}y = \dfrac{{ - 1}} {3} </var>$

 

x es fácil de sacar, reemplazando y en las ecuaciones...

 

Saludos!