1. **State the problem:** We are given the system of equations: $$x - 3y = -9$$ $$3x - 9y = 0$$ $$2x - 6y = 18$$ We need to find how many solutions $(x,y)$ satisfy all three equations simultaneously. 2. **Analyze the system:** Notice that the second and third equations can be compared to the first to check for consistency. 3. **Rewrite the first equation:** $$x - 3y = -9$$ 4. **Check if the second equation is a multiple of the first:** Multiply the first equation by 3: $$3(x - 3y) = 3(-9)$$ $$3x - 9y = -27$$ But the second equation is: $$3x - 9y = 0$$ Since $$-27 \neq 0$$, the second equation is not consistent with the first. 5. **Check if the third equation is a multiple of the first:** Multiply the first equation by 2: $$2(x - 3y) = 2(-9)$$ $$2x - 6y = -18$$ But the third equation is: $$2x - 6y = 18$$ Since $$-18 \neq 18$$, the third equation is also not consistent with the first. 6. **Conclusion:** The system is inconsistent because the second and third equations contradict the first. Therefore, there is **no solution** that satisfies all three equations simultaneously. **Final answer:** (A) Zero solutions.