Solve 6x-9xy-3xz=0

$$6 x - 9 x y - 3 x z = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=\frac{2-z}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(6-9y-3z\right)x=0$$

The equation is in standard form.

$$\left(6-3z-9y\right)x=0$$

Divide 0 by 6-9y-3z.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{2-z}{3}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$-9xy-3xz=-6x$$

Add 3xz to both sides.

$$-9xy=-6x+3xz$$

The equation is in standard form.

$$\left(-9x\right)y=3xz-6x$$

Divide both sides by -9x.

$$\frac{\left(-9x\right)y}{-9x}=\frac{3x\left(z-2\right)}{-9x}$$

Dividing by -9x undoes the multiplication by -9x.

$$y=\frac{3x\left(z-2\right)}{-9x}$$

Divide 3x\left(-2+z\right) by -9x.

$$y=\frac{2-z}{3}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=\frac{2-z}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(6-9y-3z\right)x=0$$

The equation is in standard form.

$$\left(6-3z-9y\right)x=0$$

Divide 0 by 6-9y-3z.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{2-z}{3}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$-9xy-3xz=-6x$$

Add 3xz to both sides.

$$-9xy=-6x+3xz$$

The equation is in standard form.

$$\left(-9x\right)y=3xz-6x$$

Divide both sides by -9x.

$$\frac{\left(-9x\right)y}{-9x}=\frac{3x\left(z-2\right)}{-9x}$$

Dividing by -9x undoes the multiplication by -9x.

$$y=\frac{3x\left(z-2\right)}{-9x}$$

Divide 3x\left(-2+z\right) by -9x.

$$y=\frac{2-z}{3}$$