Solve y=ax+b^8

$$y = a x + b ^ { 8 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b^{8}-y}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=b^{8}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax+b^{8}=y$$

Subtract b^{8} from both sides.

$$ax=y-b^{8}$$

The equation is in standard form.

$$xa=y-b^{8}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{y-b^{8}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{y-b^{8}}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{b^{8}-y}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=b^{8}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax+b^{8}=y$$

Subtract b^{8} from both sides.

$$ax=y-b^{8}$$

The equation is in standard form.

$$xa=y-b^{8}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{y-b^{8}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{y-b^{8}}{x}$$

Solve for b (complex solution)

$$b\in \sqrt{2}\left(\frac{1}{2}+\frac{1}{2}i\right)\sqrt[8]{y-ax},\sqrt[8]{y-ax},i\sqrt[8]{y-ax},\sqrt{2}\left(-\frac{1}{2}+\frac{1}{2}i\right)\sqrt[8]{y-ax},-\sqrt[8]{y-ax},\sqrt{2}\left(-\frac{1}{2}-\frac{1}{2}i\right)\sqrt[8]{y-ax},-i\sqrt[8]{y-ax},\sqrt{2}\left(\frac{1}{2}-\frac{1}{2}i\right)\sqrt[8]{y-ax}$$

Solve for b

$$b=\sqrt[8]{y-ax}$$

$$b=-\sqrt[8]{y-ax}\text{, }y\geq ax$$