Question

Qual das alternativas apresentam uma solução do sistema{x+y+2z=9x+2y+z=8
2x+y+z=7
alternativas
a)8,1,0
b)10,-1,0
C)1,2,3
d)9,0,0
e)1,1,1

Answer 1

Oi Thalita.

$x+y+2z=9\quad (I)\\ x+2y+z=8\quad (II)\\ 2x+y+z=7\quad (III)\\ \\ (I)+(-II)\\ \\ x+y+2z=9\\ -x-2y-z=-8\\ -y+z=1\\ \\ (2*I)+(-III)\\ \\ 2x+2y+4z=18\\ -2x-y-z=-7\\ y+3z=11\\ \\ -y+z=1\\ y+3z=11\\ 4z=12\\ z=\frac { 12 }{ 4 } \Leftrightarrow 3\\ \\ -y+3=1\\ 3-1=y\\ 2=y\\ \\ (I)\\ x+y+2z=9\\ x+2+2(3)=9\\ x=9-2-6\\ x=1\\ \\ x=1,y=2,z=3$