Solve 2x/2z=2x-y

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{yz}{1-2z}\text{, }&z\neq \frac{1}{2}\text{ and }z\neq 0\\x\in \mathrm{R}\text{, }&z=\frac{1}{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2z.

$$2x=2x\times 2z-y\times 2z$$

Multiply 2 and 2 to get 4.

$$2x=4xz-y\times 2z$$

Multiply -1 and 2 to get -2.

$$2x=4xz-2yz$$

Subtract 4xz from both sides.

$$2x-4xz=-2yz$$

Combine all terms containing x.

$$\left(2-4z\right)x=-2yz$$

Divide both sides by 2-4z.

$$\frac{\left(2-4z\right)x}{2-4z}=-\frac{2yz}{2-4z}$$

Dividing by 2-4z undoes the multiplication by 2-4z.

$$x=-\frac{2yz}{2-4z}$$

Divide -2yz by 2-4z.

$$x=-\frac{yz}{1-2z}$$

Solve for y

$$y=\frac{x\left(2z-1\right)}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2z.

$$2x=2x\times 2z-y\times 2z$$

Multiply 2 and 2 to get 4.

$$2x=4xz-y\times 2z$$

Multiply -1 and 2 to get -2.

$$2x=4xz-2yz$$

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

$$4xz-2yz=2x$$

Subtract 4xz from both sides.

$$-2yz=2x-4xz$$

The equation is in standard form.

$$\left(-2z\right)y=2x-4xz$$

Divide both sides by -2z.

$$\frac{\left(-2z\right)y}{-2z}=\frac{2x-4xz}{-2z}$$

Dividing by -2z undoes the multiplication by -2z.

$$y=\frac{2x-4xz}{-2z}$$

Divide 2x-4xz by -2z.

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