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Find All Solutions for the System {5x+5y=1025x−25y=75\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. {5x+5y=1025x−25y=75\left\{ \begin{array} { l } 5 ^ { x } + 5 ^ {y } = 10 \\25 ^ { x } - 25^ {y } = 75\end{array} \right. Note that 25x=52x=(5x)225 ^ { x } = 5 ^ { 2 x } = \left( 5 ^ { x } \right) ^ { 2 } .

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