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The given equation is:

\[
\frac{5}{a} + \frac{6}{b} = 7
\]

This equation involves two unknowns, \( a \) and \( b \), and represents a system where the sum of two fractions equals 7. 

To solve for \( a \) and \( b \), additional information or another equation is usually required. As it stands, this is an underdetermined system, meaning there are many possible solutions for \( a \) and \( b \).

Would you like to provide another equation, or should I proceed with methods for solving this type of equation (e.g., finding relationships between \( a \) and \( b \))? Feel free to clarify further!

Here are 5 possible directions we can take from this equation:
1. How can we manipulate this equation to express one variable in terms of the other?
2. What happens if we assign a specific value to one of the variables?
3. How do we solve for \( a \) or \( b \) if given a second equation?
4. Can we visualize the relationship between \( a \) and \( b \) using graphs?
5. How would this system be solved using matrix or algebraic techniques?

**Tip:** In an equation involving multiple variables, solving one variable in terms of the other can often simplify the problem.

Explore how to solve the equation 5/a + 6/b = 7 using algebraic techniques. Learn how to manipulate this equation and solve for one variable in terms of the other. Suitable for high school students (Grades 9-12).

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