Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\begin{cases}\mathsf{x + y + x = 1}\\\mathsf{x + y - z = -3}\\\mathsf{x - y + z = 3}\end{cases}[/tex]
[tex]\mathsf{\begin{bmatrix}\cancel1&\cancel1&\cancel1\\\cancel1&\cancel1&\cancel-1\\\cancel1&\cancel-1&\cancel1\end{bmatrix}}[/tex]
[tex]\mathsf{D = (1 - 1 - 1) - (1 + 1 + 1)}[/tex]
[tex]\mathsf{D = (-1) - (3)}[/tex]
[tex]\mathsf{D = -4}[/tex]
[tex]\mathsf{\begin{bmatrix}\cancel1&\cancel1&\cancel1\\\cancel-3&\cancel1&\cancel-1\\\cancel3&\cancel-1&\cancel1\end{bmatrix}}[/tex]
[tex]\mathsf{D_X = (1 - 3 + 3) - (3 + 1 - 3)}[/tex]
[tex]\mathsf{D_X = (1) - (1)}[/tex]
[tex]\mathsf{D_X = 0}[/tex]
[tex]\mathsf{\begin{bmatrix}\cancel1&\cancel1&\cancel1\\\cancel1&\cancel-3&\cancel-1\\\cancel1&\cancel3&\cancel1\end{bmatrix}}[/tex]
[tex]\mathsf{D_Y = (-3 - 1 + 3) - (-3 - 3 + 1)}[/tex]
[tex]\mathsf{D_Y = (-1) - (-5)}[/tex]
[tex]\mathsf{D_Y = (-1) + (5)}[/tex]
[tex]\mathsf{D_Y = 4}[/tex]
[tex]\mathsf{\begin{bmatrix}\cancel1&\cancel1&\cancel1\\\cancel1&\cancel1&\cancel-3\\\cancel1&\cancel-1&\cancel3\end{bmatrix}}[/tex]
[tex]\mathsf{D_Z = (3 - 3 - 1) - (1 + 3 + 3)}[/tex]
[tex]\mathsf{D_Z = (-1) - (7)}[/tex]
[tex]\mathsf{D_Z = -8}[/tex]
[tex]\mathsf{x = \dfrac{D_X}{D} = \dfrac{0}{-4} = 0}[/tex]
[tex]\mathsf{y = \dfrac{D_Y}{D} = \dfrac{4}{-4} = -1}[/tex]
[tex]\mathsf{z = \dfrac{D_Z}{D} = \dfrac{-8}{-4} = 2}[/tex]
[tex]\mathsf{x^2 + y^2 + 2z^2 = 0^2 + (-1)^2 + 2.(2)^2}[/tex]
[tex]\mathsf{x^2 + y^2 + 2z^2 = 0 + 1 + 2.(4)}[/tex]
[tex]\mathsf{x^2 + y^2 + 2z^2 = 0 + 1 + 8}[/tex]
[tex]\boxed{\boxed{\mathsf{x^2 + y^2 + 2z^2 = 9}}}\leftarrow\textsf{letra B}[/tex]
