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 $25 ^ { x } = 5 ^ { 2 x } = \left( 5 ^ { x } \right) ^ { 2 }$ .

---

Definitions:

Grammar Rules

The set of structures and guidelines that dictate the proper use of a language.

New Words

The introduction or creation of words that are not previously known or used within a language or context.

Years

Units of time equal to 365 days (or 366 days in leap years), used as a measure of time passing.

Age

The length of time that a person or object has existed, often considered in years from the date of birth for people.