\frac53x+\frac13=-\frac16x+\frac69\\\frac{11}6x=\frac13\\x=\frac{2}{11}\\y=\frac53\cdot \frac{2}{11}+\frac13=\frac{10}{33}+\frac13=\frac{7}{11}\\\boxed{C=\left(\frac{2}{11},\frac{7}{11}\right)}