1. **State the problem:** Solve the system of equations using elimination: $$-9x - 4y = -4$$ $$6x + y = 16$$ 2. **Goal:** Eliminate one variable by making the coefficients of $y$ (or $x$) opposites. 3. Multiply the second equation by 4 to align the $y$ coefficients: $$4(6x + y) = 4(16)$$ $$24x + 4y = 64$$ 4. Now add the first equation and the new equation: $$(-9x - 4y) + (24x + 4y) = -4 + 64$$ Simplify: $$(-9x + 24x) + (-4y + 4y) = 60$$ $$15x + \cancel{0} = 60$$ 5. Solve for $x$: $$15x = 60$$ $$\cancel{15}x = \cancel{60}$$ $$x = 4$$ 6. Substitute $x=4$ into the second original equation to find $y$: $$6(4) + y = 16$$ $$24 + y = 16$$ 7. Solve for $y$: $$y = 16 - 24$$ $$y = -8$$ **Final answer:** $$x = 4, \quad y = -8$$