Question

Me ajudem por favorr ..sistema linear

X + Y + 2Z = 9                                   
X+2Y+ Z = 8       
2X + Y + Z=7

Answer 1

Oi Gabriel. Vamos resolver pelo método da adição.

$\left\{ \begin{matrix} x+y+2z=9 & (I) \\ x+2y+z=8 & (II) \\ 2x+y+z=7 & (III) \end{matrix} \right.$

$(I)+(-II)\\ \\ x+y+2z=9\\ -x-2y-z=-8 \\ \boxed{\boxed {-y+z=1}}~ ~ (IV)$

$(-2*I)+(III)\\ -2x-2y-4z=-18\\ 2x+y+z=7 \\ \boxed{\boxed{-y-3z=-11}}\quad (V)$

$\\ (-IV)+(V)\\ \\ y-z=-1\\ -y-3z=-11\\ -4z=-12\quad (-1)\\ 4z=12 \\ z=\frac { 12 }{ 4 } \\ \\\Huge \boxed{\boxed {z=3}}$

$y-z=-1\\ y-3=-1\\ y=-1+3 \\ \\ \Huge \boxed{\boxed {y=2}}$

$x+y+2z=9\\ 3+2+2z=9\\ 2z=9-5\\ 2z=4\\ z=\frac { 4 }{ 2 } \\ \\ \Huge \boxed{\boxed {z=2}}$


$\Huge \boxed{\boxed{\boxed{\boxed {S={3,2,2}}}}}$