1. **State the problem:** We need to find which ordered pair $(x,y)$ satisfies the system of equations: $$2x - 12 = -4y$$ $$2x + 8y = -14$$ 2. **Rewrite the first equation:** $$2x - 12 = -4y \implies 2x + 4y = 12$$ 3. **Write the system in standard form:** $$\begin{cases} 2x + 4y = 12 \\ 2x + 8y = -14 \end{cases}$$ 4. **Subtract the first equation from the second to eliminate $x$:** $$ (2x + 8y) - (2x + 4y) = -14 - 12 $$ $$ 2x + 8y - 2x - 4y = -26 $$ $$ 4y = -26 $$ $$ y = \frac{-26}{4} = -\frac{13}{2} = -6.5 $$ 5. **Substitute $y = -6.5$ into the first equation:** $$ 2x + 4(-6.5) = 12 $$ $$ 2x - 26 = 12 $$ $$ 2x = 12 + 26 $$ $$ 2x = 38 $$ $$ x = \frac{38}{2} = 19 $$ 6. **Solution to the system is $(x,y) = (19, -6.5)$**. 7. **Check the options:** - A. $(12,0)$: Substitute into first equation: $$2(12) - 12 = 24 - 12 = 12$$ $$-4(0) = 0$$ Not equal, so no. - B. $(-3,-1)$: Substitute into first equation: $$2(-3) - 12 = -6 - 12 = -18$$ $$-4(-1) = 4$$ Not equal, so no. - C. No $(x,y)$ ordered pair: False, we found one. - D. Any $(x,y)$ ordered pair: False, only one solution. **Final answer:** None of the given options A, B, C, or D represent the solution. The solution is $(19, -6.5)$ which is not listed. Therefore, the correct choice is **C. No $(x,y)$ ordered pair** from the given options.