I am looking for a systematic way to balance chemical equations, instead of doing them by hand. Can someone help me understand the table in the How Does It Work? section at tinyurl dot com/28mngtt

I'm sorry, but as an AI text-based bot, I cannot directly access or browse the internet. Therefore, I cannot view or analyze the specific table you mentioned in your question. However, I can provide you with a general explanation of how to balance chemical equations systematically.

Balancing chemical equations involves making sure that the number of atoms on each side of the equation is equal. Here is a step-by-step approach to balancing chemical equations:

1. Write down the unbalanced equation: Start by writing the chemical equation you want to balance. For example, let's consider the equation: 2H2 + O2 -> 2H2O.

2. Count the atoms on each side: Count the number of each type of atom on both sides of the equation. In our example, there are 4 hydrogen atoms and 2 oxygen atoms on the left side, and 4 hydrogen atoms and 2 oxygen atoms on the right side.

3. Identify the imbalanced elements: Determine which elements are not balanced. In our example, it is hydrogen (H) and oxygen (O).

4. Balance the elements one at a time: Start by balancing the element that appears in the fewest compounds. In this case, let's start with hydrogen.

- To balance hydrogen, multiply the number of hydrogen atoms on each side by a coefficient to make them equal. In this example, multiply the coefficient of H2 from the left side by 2: 2H2 + O2 -> 2H2O.
- Now, there are 4 hydrogen atoms on each side.

5. Continue balancing other elements: After balancing hydrogen, move on to the next element, which is oxygen in our example.

- Multiply the coefficient of O2 from the right side by 2 to balance oxygen: 2H2 + O2 -> 2H2O.
- Now, there are 4 oxygen atoms on each side, and the equation is balanced.

6. Check the equation: Finally, double-check that the number of atoms of each element is equal on both sides.

Balancing chemical equations systematically can be done by following these steps for each element in the equation. However, without specific details about the table in the "How Does It Work?" section you mentioned, I cannot provide more specific guidance. If you have any further questions or need more assistance, feel free to ask!