[Python] Solve simultaneous equations for positive integer values
ApproachLet x be the number of jumbo burgers, y be the number of small burgers, t be the number of tomato slices, and c be the number of cheese slices.
Then, we
# Approach

Let $x$ be the number of jumbo burgers, $y$ be the number of small burgers, $t$ be the number of tomato slices, and $c$ be the number of cheese slices.
Then, we have the following simultaneous equations to satisfy:

$$
x + y = c\\
4x + 2y = t
$$

We can solve directly for $x$ and $y$ as follows:

$$
2x + y = \frac{t}{2}\\
x = \frac{t}{2} - c\\
y = c - x = 2c - \frac{t}{2}
$$

Hence, $x$ and $y$ have positive integer solutions if the following conditions hold:

- $t$ is an even number, else $\frac{t}{2}$ will not be an integer solution.
- $c \leq \frac{t}{2} \leq 2c$, else either $x$ or $y$ will be negative.

# Complexity
- Time complexity: $O(1)$

- Space complexity: $O(1)$

# Code
```python3 []
class Solution:
    def numOfBurgers(self, t: int, c: int) -> List[int]:
        return [t // 2 - c, 2 * c - t // 2] if t % 2 == 0 and c <= t // 2 <= 2 * c else []
```
['Math', 'Python3']