Question

$\sqrt{2x} + \sqrt{5y} = 16$
Is the equation a linear equation in 2 variables?
Answer with full explaination​

Answer 1

Answer:

$\mathrm{solve\:for\:x,\:\sqrt{2x}+\sqrt{5y}=16\quad :\quad x=\frac{256-32\sqrt{5}\sqrt{y}+5y}{2}\space\left\{0\le \:y\le \frac{256}{5}\right\}}$

Step-by-step explanation:

$\sqrt{2x}+\sqrt{5y}=16$

$\sqrt{2x}+\sqrt{5}\sqrt{y}=16$

$\mathrm{Subtract\:}\sqrt{5}\sqrt{y}\mathrm{\:from\:both\:sides}$

$\sqrt{2x}+\sqrt{5}\sqrt{y}-\sqrt{5}\sqrt{y}=16-\sqrt{5}\sqrt{y}$

$\sqrt{2x}=16-\sqrt{5}\sqrt{y}$

$2x=256-32\sqrt{5}\sqrt{y}+5y$

$x=\frac{256-32\sqrt{5}\sqrt{y}+5y}{2}$

$\mathrm{The\:solution\:is}$

$x=\frac{256-32\sqrt{5}\sqrt{y}+5y}{2}\space\left\{0\le \:y\le \frac{256}{5}\right\}$