1. **Stating the problem:** Solve the system of equations for part d): $$3 - 2(x - 4) = 5y + 6$$ $$5x - 3y = 12x - (4 - y)$$ 2. **Rewrite and simplify each equation:** For the first equation: $$3 - 2(x - 4) = 5y + 6$$ Distribute $-2$: $$3 - 2x + 8 = 5y + 6$$ Combine like terms: $$11 - 2x = 5y + 6$$ Subtract 6 from both sides: $$11 - 6 - 2x = 5y$$ $$5 - 2x = 5y$$ 3. **Express $y$ in terms of $x$ from the first equation:** $$5y = 5 - 2x$$ Divide both sides by 5: $$y = \frac{5 - 2x}{5}$$ 4. **Simplify the second equation:** $$5x - 3y = 12x - (4 - y)$$ Distribute the minus: $$5x - 3y = 12x - 4 + y$$ Bring all terms to one side: $$5x - 3y - 12x + 4 - y = 0$$ Combine like terms: $$-7x - 4y + 4 = 0$$ Rewrite: $$-7x - 4y = -4$$ Multiply both sides by $-1$: $$7x + 4y = 4$$ 5. **Substitute $y$ from step 3 into the second equation:** $$7x + 4 \left(\frac{5 - 2x}{5}\right) = 4$$ Multiply out: $$7x + \frac{4(5 - 2x)}{5} = 4$$ Multiply both sides by 5 to clear denominator: $$5 \times 7x + 4(5 - 2x) = 5 \times 4$$ $$35x + 20 - 8x = 20$$ Combine like terms: $$27x + 20 = 20$$ Subtract 20 from both sides: $$27x = 0$$ 6. **Solve for $x$:** $$x = 0$$ 7. **Find $y$ using $x=0$ in step 3:** $$y = \frac{5 - 2(0)}{5} = \frac{5}{5} = 1$$ **Final answer:** $$x = 0, \quad y = 1$$