sat-dog

Choice C is correct. It's given by the first equation in the system that $y=-\frac{1}{9}x$. Substituting $-\frac{1}{9}x$ for $y$ in the second equation in the system yields $-\frac{1}{9}x=\frac{1}{2}x$. Multiplying the left-hand side of this equation by $\frac{2}{2}$ and the right-hand side by $\frac{9}{9}$ yields $-\frac{2}{18}x=\frac{9}{18}x$. Adding $\frac{2}{18}x$ to both sides of this equation yields $0=\frac{11}{18}x$. Multiplying both sides of this equation by $\frac{18}{11}$ yields $x=0$.

Choice A is incorrect and may result from conceptual or calculation errors. 

Choice B is incorrect and may result from conceptual or calculation errors. 

Choice D is incorrect and may result from conceptual or calculation errors.