2015/055) Prove that equation $(3x + 4y)(4x + 5y) = 7^z$ is not possible?

we should have

$7^a$ divides $(3x+4y)$ and $7^b$ divides $(4x+5y)$

now $gcd(3x+4y, 4x+ 5y)$
$= gcd( 3x + 4y, x+ y)$
$= gcd( y, x+y)$
$= gcd(x,y)$

if 7 divides $3x + 4y$ then it does not divide $4x+ 5y$ or if it divides both x an y then sum cannot be power of 7 hence it is not possible
This I have solved at https://in.answers.yahoo.com/question/index?qid=20130925091522AAvX8Z0