Question

Find a partial differential equation by eliminating a and b from the equations of

z = ax + (1 − a)y + b.

Answer 1

Given $z = ax + (1 − a)y + b.$

Differentiating partially with respect to 'x', $p = \dfrac{\partial z}{\partial x} = a$

Differentiating partially with respect to 'y', $q = \dfrac{\partial z}{\partial y} = 1-a$

Eliminating 'a' from these we get, $p + q = 1$, which is the required partial differential equation.