Question

gauss 2x+y=8 abajo x_ 4y=_5​

Answer 1

Sistema de ecuaciones:

$\mathsf{ 2x+y = 8 }$

$\mathsf{ x-4y = -5 }$

Eliminación de Gauss-Jordan

${\displaystyle \left({\begin{array}{rrrr}2&1&| &8\\1&-4&|&-5\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}8&4&| &32\\1&-4&|&-5\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}9&0&| &27\\1&-4&|&-5\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}1&0&| &3\\1&-4&|&-5\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}1&0&| &3\\-1&4&|&5\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}1&0&| &3\\0&4&|&8\end{array}}\right)}$

${\displaystyle \left({\begin{array}{rrrr}1&0&| &3\\0&1&|&2\end{array}}\right)}$

Entonces:

$\mathsf{ x = 3 }$

$\mathsf{ y = 2 }$