If 2 x+y=15,2 y+z=25 and 2 z+x=26, what is the value of z ? · ABC26GN1055

$2 x+y=15$ $$2 y+z=25$$ and $2 z+x=26$ Adding (i), (ii) and (iii), we get: $3(x+y+z)$ $$=66 \text { or } x+y+z=22$$ From (ii), we have: $y=\frac{25-z}{2}$. From (iii), we have: $$\begin{aligned} & x=26-2 z . \\ & \therefore \quad(26-2 z)+\left(\frac{25-z}{2}\right)+z=22 \Leftrightarrow 77-3 z=44 \\ & \Leftrightarrow \quad 3 z=33 \Leftrightarrow z=11 . \end{aligned}$$