Verified answer

Resposta:

[tex]\Large \textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\Large \text{$ \begin{cases}\sf 3x + 4y - z = 1\\\sf 2x - y + 5z = 3\\\sf x + y + z = 2\end{cases}$}[/tex]

[tex]\Large \text{$ \sf L1 + L3$}[/tex]

[tex]\Large \text{$ \sf 4x + 5y = 3$}[/tex]

[tex]\Large \text{$ \sf L2 - 5\:.\:L3$}[/tex]

[tex]\Large \text{$ \sf 3x + 6y = 7$}[/tex]

[tex]\Large \text{$ \begin{cases}\sf 4x + 5y = 3\\\sf 3x + 6y = 7\end{cases}$}[/tex]

[tex]\Large \text{$ \sf 3\:.\:L1 - 4\:.\:L2$}[/tex]

[tex]\Large \text{$ \sf 9y = 19$}[/tex]

[tex]\Large \boxed{\text{$ \sf y = \dfrac{19}{9}$}}[/tex]

[tex]\Large \text{$ \sf 4x + 5\left(\dfrac{19}{9}\right) = 3$}[/tex]

[tex]\Large \text{$ \sf 36x + 95 = 27$}[/tex]

[tex]\Large \text{$ \sf 36x = - 68 $}[/tex]

[tex]\Large \boxed{\text{$ \sf x = -\dfrac{17}{9}$}}[/tex]

[tex]\Large \text{$ \sf -\dfrac{17}{9} + \dfrac{19}{9} + z = 2$}[/tex]

[tex]\Large \text{$ \sf -17 + 19 + 9z = 18$}[/tex]

[tex]\Large \text{$ \sf 9z = 16$}[/tex]

[tex]\Large \boxed{\text{$ \sf z = \dfrac{16}{9}$}}[/tex]