1. **State the problem:** Solve the simultaneous equations: $$y - 4x = 16$$ and $$\frac{y + 24}{3x - 6} = 4$$ 2. **Express $y$ from the first equation:** $$y = 4x + 16$$ 3. **Substitute $y$ into the second equation:** $$\frac{(4x + 16) + 24}{3x - 6} = 4$$ Simplify numerator: $$\frac{4x + 40}{3x - 6} = 4$$ 4. **Multiply both sides by $3x - 6$ to clear the denominator:** $$4x + 40 = 4(3x - 6)$$ 5. **Expand the right side:** $$4x + 40 = 12x - 24$$ 6. **Bring all terms to one side:** $$4x + 40 - 12x + 24 = 0$$ Simplify: $$-8x + 64 = 0$$ 7. **Solve for $x$:** $$-8x = -64$$ Intermediate step showing cancellation: $$\cancel{-8}x = \cancel{-8}8$$ So, $$x = 8$$ 8. **Substitute $x=8$ back into $y = 4x + 16$ to find $y$:** $$y = 4(8) + 16 = 32 + 16 = 48$$ **Final answer:** $$x = 8, \quad y = 48$$