Definiton of a$\displaystyle a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b$ where $\displaystyle b$ is alinear equation

real number

Note if $\displaystyle b = 0$, it's ahomogeneous equation.

What are some reasons why these statements are true?

$\displaystyle 3x - 4xy = 0$ -not linear

$\displaystyle x^{2} + y^{2} = 4$ -not linear

$\displaystyle (\sin2x) - y = 14$linear