Question

Resolva os seguintes sistemas:


a)

{ 3× -2y = 0

x + y = 5


b)

{ x +y +z = 6

2× -y +z = 3

x + 4y -z = 6


respostas com contas por favor.

me ajudem se puderem :) ♡

Answer 1

Resposta:

Explicação passo a passo:

Resolvendo:

I.

$\left \{ {{3x-2y=0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:} \atop {x+y=5\:\:-->\:\:x=5-y}} \right. \\\\3x-2y=0\\3(5-y)-2y=0\\15-3y-2y=0\\-5y=-15\\y= 3\\\\x+y=5\\x+3=5\\x=2$

S = { (2; 3) }

II.

$\left \{ {{x+y+z=6\:\:-->\:\:x=6-z-y} \atop {2x-y+z=3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}} \right. \\x+4y-z=6\\\\Substituindo:\\\\2x-y+z=3\\2(6-z-y)-y+z=3\\12-2z-2y-y+z=3\\-z-3y=-9\\\\x+4y-z=6\\6-z-y+4y-z=6\\3y-2z=0\\\\Novo\:\:sistema:\\\\\left \{ {{-z-3y=-9} \atop {3y-2z=0}} \right. \\+-----\\-3z=-9\\z=3\\\\3y-2z=0\\3y-2\:.\:3=0\\3y-6=0\\3y=6\\y=2\\\\Agora, \:descobriremos\:x:\\\\x+y+z=6\\x+2+3=6\\x+5=6\\x=1$

S = { (1; 2; 3) }

Espero ter ajudado!

Desculpe qualquer erro.