1. **State the problem:** We need to find the cost of each item sold separately: small pizza ($x$), liter of soda ($y$), and salad ($z$). 2. **Write the system of equations from the problem:** $$\begin{cases} 2x + y + z = 14 \\ x + y + 3z = 15 \\ 3x + y = 16 \end{cases}$$ 3. **Explain the approach:** We will solve this system using substitution or elimination to find $x$, $y$, and $z$. 4. **From the third equation, express $y$ in terms of $x$:** $$y = 16 - 3x$$ 5. **Substitute $y$ into the first two equations:** - First equation: $$2x + (16 - 3x) + z = 14 \implies 2x + 16 - 3x + z = 14 \implies -x + z = -2 \implies z = x - 2$$ - Second equation: $$x + (16 - 3x) + 3z = 15 \implies x + 16 - 3x + 3z = 15 \implies -2x + 3z = -1$$ 6. **Substitute $z = x - 2$ into the second equation:** $$-2x + 3(x - 2) = -1 \implies -2x + 3x - 6 = -1 \implies x - 6 = -1 \implies x = 5$$ 7. **Find $z$ using $z = x - 2$:** $$z = 5 - 2 = 3$$ 8. **Find $y$ using $y = 16 - 3x$:** $$y = 16 - 3(5) = 16 - 15 = 1$$ 9. **Final answer:** - Small pizza ($x$) costs 5 - Liter of soda ($y$) costs 1 - Salad ($z$) costs 3