Solve {l}{a_{1}q^2+a_{1}q^5=3b}{a_{1}q^3+a_{1}q^6=18}

$$\left\{ \begin{array} { l } { a _ { 1 } q ^ { 2 } + a _ { 1 } q ^ { 5 } = 3 b } \\ { a _ { 1 } q ^ { 3 } + a _ { 1 } q ^ { 6 } = 18 } \end{array} \right.$$

Solve for a_1, q, b (complex solution)

$$a_{1}=\frac{18}{q^{3}\left(q^{3}+1\right)}$$

$$q\in \mathrm{C}\setminus 0,-1,\frac{1+\sqrt{3}i}{2},\frac{-\sqrt{3}i+1}{2}$$

$$b=\frac{6}{q}$$

Solve for a_1, q, b

$$a_{1}=\frac{18}{q^{3}\left(q^{3}+1\right)}$$

$$q\in \mathrm{R}\setminus -1,0$$

$$b=\frac{6}{q}$$