9B = A
10a - 9B = B
9B² = 10a² - 9ab

Let's take a look at the equations provided:

Equation 1: 9 B = A
Equation 2: 10 a − 9 B = B
Equation 3: 9 B 2 = 10 a 2 − 9 ab

Let's go through these equations one by one to understand them clearly:
Equation 1: 9 B = A
This equation indicates a simple relationship between two variables, A and B . It suggests that A is 9 times B .
Equation 2: 10 a − 9 B = B
In this equation, we have three variables: a , B , and B . This can be rewritten to solve for one of the variables, say a :
10 a − B = 9 B 10 a = 10 B a = B Thus, a = B .
Equation 3: 9 B 2 = 10 a 2 − 9 ab
This is a quadratic equation involving B and a . We can substitute a = B from the Equation 2 into this equation:
9 B 2 = 10 ( B ) 2 − 9 B ( B ) 9 B 2 = 10 B 2 − 9 B 2 9 B 2 = 1 B 2 This simplifies to an identity where both sides are equal (assuming the operations are consistent).
Conclusion
From these analyses, here’s what we understand:

The equations involve three variables ( A , a and B ) where A is 9 times B and a equals B .
The given equations, when simplified, show consistency and balance.

This exercise could be related to understanding relationships among variables, simplifying equations, and recognizing identities in mathematics.

Answered by IsabellaRoseDavis | 2025-07-06