\[
\begin{array}{l}
X^{\prime}=x(1-x)+0.5 x y \\
Y^{\prime}=y(2.5-1.5 y)+0.25 x y
\end{array}
\]
Classify the equilibrium points for the system . using latex editor

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Answer

\( (x, y) = (0, 0), (1, 0), \left( 0, \frac{5}{3} \right) \)

Steps

Step 1 ：\( X' = x(1-x) + 0.5xy = 0 \)

Step 2 ：\( Y' = y(2.5 - 1.5y) + 0.25xy = 0 \)

Step 3 ：\( (x, y) = (0, 0), (1, 0), \left( 0, \frac{5}{3} \right) \)