To complete the system of inequalities representing when the natural gas supply will adequately meet the needs of the population, we can analyze the provided inequalities.
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The first inequality is given as: \[ y \leq 0.9x \] This means that the population \(y\) should not exceed \(0.9\) times the variable \(x\) (which could represent some factor related to population, such as time, resource consumption, etc.).
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The second inequality is given as: \[ y \geq 1 - x \] This implies that the population \(y\) should be at least \(1 - x\), indicating the minimum population that can be supported by the natural gas supply.
With these interpretations, the complete system of inequalities is:
\[ \begin{cases} y \leq 0.9x \ y \geq 1 - x \end{cases} \]
This system will represent the values of \(y\) where the population can be supported by the natural gas supply, depending on the value of \(x\). The area where both inequalities hold true will indicate when the gas supply can adequately meet the needs of the population.