1. **State the problem:** Solve the system of linear equations: $$-\frac{1}{4}x + 3y = 6$$ $$-2x + 24y = 48$$ 2. **Rewrite the first equation to eliminate fractions:** Multiply both sides of the first equation by 4 to clear the denominator: $$4 \times \left(-\frac{1}{4}x + 3y\right) = 4 \times 6$$ $$\cancel{4} \times -\frac{1}{\cancel{4}}x + 4 \times 3y = 24$$ $$-x + 12y = 24$$ 3. **Rewrite the system:** $$-x + 12y = 24$$ $$-2x + 24y = 48$$ 4. **Use substitution or elimination. Here, use elimination:** Multiply the first equation by 2 to align coefficients of $x$: $$2 \times (-x + 12y) = 2 \times 24$$ $$-2x + 24y = 48$$ 5. **Subtract the second equation from this new equation:** $$(-2x + 24y) - (-2x + 24y) = 48 - 48$$ $$0 = 0$$ 6. **Interpretation:** The two equations are dependent (the second is just twice the first). This means there are infinitely many solutions along the line defined by one of the equations. 7. **Express $x$ in terms of $y$ from the first simplified equation:** $$-x + 12y = 24$$ $$-x = 24 - 12y$$ $$x = -24 + 12y$$ **Final answer:** The solution set is all points $(x,y)$ such that $$x = -24 + 12y$$ for any real number $y$.