1. **State the problem:** Find the ordered pair $(x,y)$ that satisfies both equations: $$-6x - 7y = 0$$ $$4x - 5y = 58$$ 2. **Use the substitution or elimination method:** Here, we use elimination. 3. Multiply the first equation by 4 and the second by 6 to align coefficients of $x$: $$4(-6x - 7y) = 4(0) \Rightarrow -24x - 28y = 0$$ $$6(4x - 5y) = 6(58) \Rightarrow 24x - 30y = 348$$ 4. Add the two equations to eliminate $x$: $$(-24x - 28y) + (24x - 30y) = 0 + 348$$ $$-24x + 24x - 28y - 30y = 348$$ $$-58y = 348$$ 5. Solve for $y$: $$y = \frac{348}{-58} = \frac{\cancel{58}6}{-\cancel{58}1} = -6$$ 6. Substitute $y = -6$ into the first equation to find $x$: $$-6x - 7(-6) = 0$$ $$-6x + 42 = 0$$ 7. Solve for $x$: $$-6x = -42$$ $$x = \frac{-42}{-6} = \frac{\cancel{6}(-7)}{-\cancel{6}1} = 7$$ 8. **Final answer:** The ordered pair is $(7, -6)$. This corresponds to option [D].