1. **State the problem:** Solve the system of equations by elimination: $$8x - 8y = -16$$ $$-2x + 6y = -12$$ 2. **Goal:** Combine the equations to eliminate one variable. 3. **Multiply the second equation by 4** to align coefficients of $x$: $$4 \times (-2x + 6y) = 4 \times (-12)$$ $$-8x + 24y = -48$$ 4. **Add the first equation and the new equation:** $$\begin{aligned} &(8x - 8y) + (-8x + 24y) = -16 + (-48) \\ &\cancel{8x} - 8y - \cancel{8x} + 24y = -64 \\ &(-8y + 24y) = -64 \\ &16y = -64 \end{aligned}$$ 5. **Solve for $y$:** $$y = \frac{-64}{16} = -4$$ 6. **Substitute $y = -4$ into the first equation:** $$8x - 8(-4) = -16$$ $$8x + 32 = -16$$ 7. **Solve for $x$:** $$8x = -16 - 32$$ $$8x = -48$$ $$x = \frac{-48}{8} = -6$$ **Final answer:** $$x = -6, \quad y = -4$$ **Fill in the blanks for the elimination step:** $$8x - 8y = -16$$ $$-2x + 6y = -12$$ $$\underline{+ (-8x + 24y = -48)}$$ $$0x + 16y = -64$$