If $x+y+z=25, x+y=19$ and $y+z=18$, then $y$ equals
(A) 13
(B) 17
(C) 12
(D) 6
(E) -6
If $x+y+z=25, x+y=19$ and $y+z=18$, then $y$ equals
(A) 13
(B) 17
(C) 12
(D) 6
(E) -6

## Solution

We are given that $x+y+z=25$ (1)

$$
\begin{aligned}
& x+y=19 \\
& y+z=18
\end{aligned}
$$

Add equations (2) and (3) to get $x+2 y+z=37$ (4). Subtract equation (1) from equation (4) to get $y=12$.

ANSWER: (C)