Solve 2^x+2y=2016

$${ 2 }^{ x } +2y=2016$$

Solve for y

$$y=-\frac{2^{x}}{2}+1008$$

Steps for Solving Linear Equation

Subtract 2^{x} from both sides.

$$2y=2016-2^{x}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{2016-2^{x}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{2016-2^{x}}{2}$$

Divide 2016-2^{x} by 2.

$$y=-\frac{2^{x}}{2}+1008$$

Solve for x (complex solution)

$$x=\log_{2}\left(2016-2y\right)+\frac{2i\pi n_{1}}{\ln(2)}$$

$$n_{1}\in \mathrm{Z}$$

$$y\neq 1008$$

Solve for x

$$x=\log_{2}\left(2016-2y\right)$$

$$y<1008$$