If $3 x-4 y+z=7 ; 2 x-z+3 y=19 ; x+2 y+2 z=$ 24 , then what is the value of $z$ ?
(a)4
(b)5
(c)6
(d)8
Answer
Answer (as printed): B
Explanation
$3 x-4 y+z=7$ $$2 x+3 y-z=19$$ and $x+2 y+2 z=24$ Adding (i) and (ii), we get: $5 x-y=26$ Subtracting (i) from (ii) and adding to (iii), we get: $9 y=36$ or $y=4$. Putting $y=4$ in (iv), we get: $5 x=30$ or $x=6$. Putting $x=6, y=4$ in (iii), we get: $2 z=10$ or $z=5$.
Explanation as extracted from the printed page; notation may be imperfect.