1. **State the problem:** Solve the system of equations by elimination: $$13x + 48 = 8y$$ $$12 - 2y = - \frac{13}{4} x$$ 2. **Rewrite equations in standard form:** From the first equation: $$13x + 48 = 8y \implies 13x - 8y = -48$$ From the second equation: $$12 - 2y = - \frac{13}{4} x \implies 12 - 2y + \frac{13}{4} x = 0$$ Multiply both sides by 4 to clear the fraction: $$4 \times 12 - 4 \times 2y + 4 \times \frac{13}{4} x = 0 \implies 48 - 8y + 13x = 0$$ Rearranged: $$13x - 8y = -48$$ 3. **Compare the two equations:** Both equations simplify to: $$13x - 8y = -48$$ 4. **Interpretation:** Since both equations represent the same line, there are infinitely many solutions. 5. **Answer:** The system has an infinite number of solutions. **Final answer:** C) Infinite number of solutions