I am struggling with teaching my 9th grade kid to solve math problems that are just outside of routine.
An example problem given by math teacher at school.
x, y, z are in geometric progression
x + y + z = C1
x * x + y * y + z * z = C2
Find x, y, z.
My solution (after a couple of failed attempts) for this involves recognizing some patterns
(x + y + z)^2 = ...
Expressing x, y, z as a/r, a, ar
A bit of manipulation of  so that I can reuse x + y + z = C1 and eliminate r from the equation and find a.
How does one teach students to independently solve these problems? Are students "wired" to solve these v/s not?