Exercise Set 1.1 – No. 2

2. In each part, determine whether the equation is linear in x and y.

\large {\color{blue} (a) \; 2^{\frac{1}{3}}x+\sqrt{3}y=1}

The equation \large {\color{blue}2^{\frac{1}{3}}x+\sqrt{3}y=1} is linear in x and y.

\large {\color{blue} (b) \; 2x^{\frac{1}{3}}+\sqrt[3]{y}=1}

The equation \large {\color{blue}2x^{\frac{1}{3}}+\sqrt[3]{y}=1} is not linear x and y due to the terms \large {\color{blue}x^{\frac{1}{3}}} and \large {\color{blue}\sqrt[3]{y}}.

\large {\color{blue} (c) \;cos(\frac{\pi }{7})x-4y=log3}

The equation \large {\color{blue}\;cos({\frac{\pi}{7}})x-4y} is linear in and x and y.

\large {\color{blue}(d)\;{\frac{\pi}{7}}cosx-4y=0}

The equation \large {\color{blue}{\frac{\pi}{7}}cosx-4y=0} is not linear in x and y due to the term cosx.

(e) xy = 1

The equation xy = 1 is not linear in x and y due to the term xy.

(f ) y + 7 = x

The equation y + 7 = x is linear in x and y.