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:

Net Profit Margin

A profitability ratio that measures the percentage of each sales dollar that remains as profit after all expenses, including taxes, have been paid.

Net Income

The total profit of a business after subtracting all expenses from total revenues.

Operating Income

The profit realized from a business's operations after deducting operating expenses such as wages, depreciation, and cost of goods sold.

Inventory Turnover

A financial ratio that measures the number of times a company’s inventory is sold and replaced over a specific period, reflecting the efficiency of inventory management.