Solve sqrt{2}y*x=4sqrt{3}yz

$$\sqrt{ 2 } y \times x = 4 \sqrt{ 3 } yz$$

Solve for x

$$\left\{\begin{matrix}\\x=2\sqrt{6}z\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{2}yx=4\sqrt{3}yz$$

Divide both sides by \sqrt{2}y.

$$\frac{\sqrt{2}yx}{\sqrt{2}y}=\frac{4\sqrt{3}yz}{\sqrt{2}y}$$

Dividing by \sqrt{2}y undoes the multiplication by \sqrt{2}y.

$$x=\frac{4\sqrt{3}yz}{\sqrt{2}y}$$

Divide 4\sqrt{3}yz by \sqrt{2}y.

$$x=2\sqrt{6}z$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=2\sqrt{6}z\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4\sqrt{3}yz from both sides.

$$\sqrt{2}yx-4\sqrt{3}yz=0$$

Combine all terms containing y.

$$\left(\sqrt{2}x-4\sqrt{3}z\right)y=0$$

Divide 0 by \sqrt{2}x-4\sqrt{3}z.

$$y=0$$