Find All Solutions for the System $\left\{ \begin{array} { l } 5 ^ { x } + 5 ^ {y } = 10 \\25 ^ { x } - 25^ {y } = 75\end{array} \right.$

question 36

Essay

Find all solutions for the system. $\left\{ \begin{array} { l } 5 ^ { x } + 5 ^ {y } = 10 \\25 ^ { x } - 25^ {y } = 75\end{array} \right.$ Note that $25 ^ { x } = 5 ^ { 2 x } = \left( 5 ^ { x } \right) ^ { 2 }$ .

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Definitions:

Spouse's Death

The event of a husband or wife passing away, impacting the surviving partner's emotional, social, and financial status.

Introspection

The examination or observation of one's own mental and emotional processes.

Widows

Women whose spouses have died and who have not remarried, often facing specific social, economic, and emotional challenges.

Submerged Aspects

The parts of oneself or a situation that are not immediately visible or recognized, often holding significant influence despite being overlooked.