Which of the following represents the solution of the given system of linear equations?

3x + y + 5z = 30

2x + 2y + 3z = 40

x + y + 2z = 20

Correct option is B

​$$\begin{aligned}&\text{From Equation (3):} \\&\quad x = 20 - y - 2z \quad \text{(4)} \\[10pt]&\text{Substitute Equation (4) into (1) and (2)} \\[5pt]&\text{Substituting into Equation (1):} \\&\quad 3(20 - y - 2z) + y + 5z = 30 \\&\quad 60 - 3y - 6z + y + 5z = 30 \\&\quad 60 - 2y - z = 30 \Rightarrow 2y + z = 30 \quad \text{(5)} \\[10pt]&\text{Substituting into Equation (2):} \\&\quad 2(20 - y - 2z) + 2y + 3z = 40 \\&\quad 40 - 2y - 4z + 2y + 3z = 40 \\&\quad 40 - z = 40 \Rightarrow z = 0 \quad \text{(6)} \\[10pt]&\text{Substitute } z = 0 \text{ into Equation (5)} \\&\quad 2y + 0 = 30 \Rightarrow y = 15 \\[10pt]&\text{Substitute } y = 15,\, z = 0 \text{ into Equation (4) to find } x \\&\quad x = 20 - 15 - 2(0) = 5\end{aligned}$$​​