Solve x-y=frac{sqrt{x^2}}{9}

$$x-y= \frac{ \sqrt{ { x }^{ 2 } } }{ 9 }$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{x^{2}}}{9}+x$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9.

$$9x-9y=\sqrt{x^{2}}$$

Subtract 9x from both sides.

$$-9y=\sqrt{x^{2}}-9x$$

Divide both sides by -9.

$$\frac{-9y}{-9}=\frac{\sqrt{x^{2}}-9x}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$y=\frac{\sqrt{x^{2}}-9x}{-9}$$

Divide \sqrt{x^{2}}-9x by -9.

$$y=-\frac{\sqrt{x^{2}}}{9}+x$$

Solve for y

$$y=-\frac{|x|}{9}+x$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9.

$$9x-9y=\sqrt{x^{2}}$$

Subtract 9x from both sides.

$$-9y=\sqrt{x^{2}}-9x$$

Divide both sides by -9.

$$\frac{-9y}{-9}=\frac{|x|-9x}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$y=\frac{|x|-9x}{-9}$$

Divide |x|-9x by -9.

$$y=-\frac{|x|}{9}+x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{9y}{10}\text{, }&y=0\text{ or }arg(y)\geq \pi \\x=\frac{9y}{8}\text{, }&y=0\text{ or }arg(y)<\pi \end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{9y}{8}\text{, }&y\geq 0\\x=\frac{9y}{10}\text{, }&y\leq 0\end{matrix}\right.$$