1. **State the problem:** We are given two equations: $$0 = \frac{7.6}{1+\frac{x}{1000}} \cdot \frac{7.6}{1+y}$$ and $$0.5 = \frac{7.6}{1+\frac{x}{1304}} \cdot \frac{7.6}{1+y}$$ We want to analyze and solve these equations for $x$ and $y$. 2. **Analyze the first equation:** $$0 = \frac{7.6}{1+\frac{x}{1000}} \cdot \frac{7.6}{1+y}$$ Since $7.6$ is a positive constant, the product of two positive fractions can only be zero if one of the denominators is infinite or the expression is undefined. But denominators cannot be zero (division by zero is undefined). Therefore, the product cannot be zero unless one of the terms is zero, which is impossible here. Hence, the first equation has no solution for finite $x$ and $y$. 3. **Analyze the second equation:** $$0.5 = \frac{7.6}{1+\frac{x}{1304}} \cdot \frac{7.6}{1+y}$$ Rewrite denominators: $$\frac{7.6}{1+\frac{x}{1304}} = \frac{7.6}{\frac{1304+x}{1304}} = \frac{7.6 \cdot 1304}{1304 + x}$$ Similarly, $$\frac{7.6}{1+y}$$ So the equation becomes: $$0.5 = \frac{7.6 \cdot 1304}{1304 + x} \cdot \frac{7.6}{1+y}$$ Multiply constants: $$7.6 \times 7.6 = 57.76$$ So: $$0.5 = \frac{57.76 \cdot 1304}{(1304 + x)(1+y)}$$ Simplify numerator: $$57.76 \times 1304 = 75356.48$$ Therefore: $$0.5 = \frac{75356.48}{(1304 + x)(1+y)}$$ Cross-multiplied: $$(1304 + x)(1+y) = \frac{75356.48}{0.5} = 150712.96$$ 4. **Summary:** - The first equation has no finite solution. - The second equation relates $x$ and $y$ by: $$ (1304 + x)(1 + y) = 150712.96 $$ This is the simplified form of the second equation. **Final answer:** $$ (1304 + x)(1 + y) = 150712.96 $$