1. **Problem statement:** We have two wine packages with different numbers of bottles and total prices. We want to find the price of one bottle of red wine and one bottle of white wine. 2. **Define variables:** Let $x$ be the price of one bottle of red wine and $y$ be the price of one bottle of white wine. 3. **Set up equations from the offers:** - Angebot 1: 4 bottles of red wine and 3 bottles of white wine cost 14. $$4x + 3y = 14$$ - Angebot 2: 5 bottles of red wine and 4 bottles of white wine cost 18. $$5x + 4y = 18$$ 4. **Use the Gleichsetzungsverfahren (equalization method):** - From the first equation, solve for $y$: $$4x + 3y = 14 \Rightarrow 3y = 14 - 4x \Rightarrow y = \frac{14 - 4x}{3}$$ - From the second equation, solve for $y$: $$5x + 4y = 18 \Rightarrow 4y = 18 - 5x \Rightarrow y = \frac{18 - 5x}{4}$$ 5. **Set the two expressions for $y$ equal:** $$\frac{14 - 4x}{3} = \frac{18 - 5x}{4}$$ 6. **Cross-multiply to solve for $x$:** $$4(14 - 4x) = 3(18 - 5x)$$ $$56 - 16x = 54 - 15x$$ 7. **Isolate $x$:** $$56 - 16x = 54 - 15x$$ $$56 - 54 = -15x + 16x$$ $$2 = x$$ 8. **Substitute $x=2$ back to find $y$:** $$y = \frac{14 - 4(2)}{3} = \frac{14 - 8}{3} = \frac{6}{3} = 2$$ 9. **Answer:** Each bottle of red wine costs $2$ and each bottle of white wine costs $2$.