I don't know how to solve system of equations using CRT when there is some quadratic/cubic variable. For example:
System 1: $$\boxed{x^3 \equiv 1 \pmod{3}}$$ $$12x \equiv 9 \pmod{15}$$
System 2: $$3x \equiv 6 \pmod{9}$$ $$\boxed{x^2 \equiv 1 \pmod{4}}$$ $$4x \equiv 2 \pmod{5}$$
I think (please correct me if I'm wrong) the quadratic equation from System 2 can be rewritten into linear equations as $x \equiv \pm 1 \pmod{2}$.
How can I rewrite the cubic equation from System 1 into linear equations to be able to use CRT?
Every number is congruent to either 0,1 or 2 mod 3. The only option which cubes to 1 mod 3 is 1. Therefore x must be 1 mod 3