1. **State the problem:** Solve the system of linear equations by elimination for the first box labeled "THE": $$\begin{cases} 5x - 2y = -6 \\ x + y = -6 \end{cases}$$ 2. **Write the elimination method formula:** To eliminate one variable, multiply one or both equations so that adding or subtracting them cancels out one variable. 3. **Multiply the second equation by 2 to align coefficients of $y$:** $$\begin{cases} 5x - 2y = -6 \\ 2x + 2y = -12 \end{cases}$$ 4. **Add the two equations to eliminate $y$:** $$ (5x - 2y) + (2x + 2y) = -6 + (-12) $$ $$ 5x + 2x + (-2y + 2y) = -18 $$ $$ 7x + \cancel{-2y + 2y} = -18 $$ $$ 7x = -18 $$ 5. **Solve for $x$:** $$ x = \frac{-18}{7} $$ 6. **Substitute $x$ back into the second original equation to find $y$:** $$ x + y = -6 $$ $$ \frac{-18}{7} + y = -6 $$ $$ y = -6 + \frac{18}{7} = \frac{-42}{7} + \frac{18}{7} = \frac{-24}{7} $$ 7. **Solution for the system is:** $$ \left( \frac{-18}{7}, \frac{-24}{7} \right) $$ 8. **Check if this solution matches any coordinate in the Answer Box:** The Answer Box contains (4,2), (7,-2), (4,0), (1,4), (9,5). None match the fraction solution. Since the problem asks to solve the first system only, and the solution does not match any given coordinate, the answer is the exact solution above. **Final answer:** $\left( \frac{-18}{7}, \frac{-24}{7} \right)$