If $2 x+3 y=31, y-z=4$ and $x+2 z=11$, then what is the value of $x+y+z$ ?
(a)12
(b)13
(c)15
(d)16
Answer
Answer (as printed): C
Explanation
$2 x+3 y=31$ and $x+2 z=11$ Multiplying (iii) by 2 and subtracting from (i), we get: $$3 y-4 z=9$$ Solving (ii) and (iv), we get: $y=7, z=3$. Putting $y=7$ in (i), we get: $x=5$. $$\therefore \quad x+y+z=(5+7+3)=15 .$$
Explanation as extracted from the printed page; notation may be imperfect.