1. **State the problem:** Solve the system of equations: $$x = 8y + 32$$ $$7x - 3y = 12$$ 2. **Substitute** the expression for $x$ from the first equation into the second equation: $$7(8y + 32) - 3y = 12$$ 3. **Expand** the terms: $$56y + 224 - 3y = 12$$ 4. **Combine like terms:** $$53y + 224 = 12$$ 5. **Isolate** $y$ by subtracting 224 from both sides: $$53y + \cancel{224} - \cancel{224} = 12 - 224$$ $$53y = -212$$ 6. **Solve for** $y$ by dividing both sides by 53: $$\frac{53y}{\cancel{53}} = \frac{-212}{\cancel{53}}$$ $$y = -4$$ 7. **Substitute** $y = -4$ back into the first equation to find $x$: $$x = 8(-4) + 32$$ $$x = -32 + 32$$ $$x = 0$$ **Final answer:** The solution to the system is $\boxed{(0, -4)}$.