Question

Realice los siguientes sistemas de ecuaciones por el método de sustitución
Primera
$2 \times + 2y = 1 \\ 3 \times + 2y = 4$
Segunda
$2w + 5z = - 24 \\ 8w - 3z = 19$
​

Answer 1

Respuesta:

$1)~~x=3~~,~~~~y=-\cfrac{5}{2}$

$2)~~w=\cfrac{1}{2}~~,~~~~z=-5$

Explicación paso a paso:

1)

    $2x+2y=1~~~~~.....(1)\\3x+2y=4~~~~~.....(2)$

    Despejando y en (1):

       $2x+2y=1\\\\2y=1-2x\\\\y=\cfrac{1-2x}{2}~~~~~.....(3)$

    Sustituyendo (3) en (2):

         $3x+2y=4\\\\3x+2\cdot(\cfrac{1-2x}{2})=4\\\\3x+\cfrac{2-4x}{2}=4\\\\\cfrac{~6x+2-4x~}{2}=4\\\\6x+2-4x=4\cdot2\\\\2x+2=8\\\\2x=8-2\\\\x=\cfrac{~6~}{2}\\\\x=3$                                         $2x+2y=1\\\\2\cdot(3)+2y=1\\\\6+2y=1\\\\2y=1-6\\\\y=-\cfrac{5}{2}$

2)

      $2w+5z=-24~~~~~.....(1)\\8w-3z=19~~~~~.....(2)$

     Despejamos z en (1):

        $2w+5z=-24\\\\5z=-24-2w\\\\z=\cfrac{-24-2w}{5}~~~~~.....(3)$

    Sustituyendo (3) en (2):

       $8w-3z=19\\\\8w-3\cdot(\cfrac{-24-2w~}{5})=19\\\\8w-\cfrac{-72-6w~}{5}=19\\\\\cfrac{40w+72+6w}{5}=19\\\\40w+72+6w=5(19)\\\\46w+72=95\\\\46w=95-72\\\\w=\cfrac{23}{46}\\\\w=\cfrac{1}{2}$                   $2w+5z=-24\\\\2(\cfrac{~1~}{2})+5z=-24\\\\1+5z=-24\\\\5z=-24-1\\\\z=\cfrac{-25}{5}\\\\z=-5$