Need help solving system of 3 equations for 3 unknown variables

Question

I have the following system of equations and need to solve for A,B,C: $$2B+3C = 0$$ $$2B+9A = 3$$ $$6A +2C+6B = 0$$

I tried solving this but cannot get it to work out. Any help is much appreciated. Thank you.

Answer 1

$$C=\dfrac{2B}{3}$$ $$A=\dfrac{3-2B}{9}$$ $$6\dfrac{3-2B}{9}+2\dfrac{2B}{3}+6B=0$$

now you can solve the last equation for B then find A and C from first and second equation

Answer 2

Also from linear algebra, you can always take the row reduced echelon form $(RREF)$ of the augmented matrix $\begin{bmatrix}0 & 2 & 3 & 0 \\9&2&0&3\\6&6&2&0\end{bmatrix}$ to see that you get the correct answers.