Word Count : 353

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a) Consider the function $$ z = -x^2 + xy - y^2 + x + 5y $$ To find stationary points, compute partial derivatives: $$ \frac{\partial z}{\partial x} = -2x + y + 1, \quad \frac{\partial z}{\partial y} = x - 2y + 5 $$ Set both equal to zero: $$ -2x + y + 1 = 0 \quad \Rightarrow \quad y = 2x - 1 $$ $$ x - 2y + 5 = 0 \quad \Rightarrow \quad x = 2y - 5 $$ Substitute $y = 2x ____ ________ ________ __________ ____.
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