Solve y/1-yleft(1-4zright)/5=4{x}_{2}

$$\frac{ y }{ 1 } - \frac{ y \left( 1-4z \right) }{ 5 } = 4 { x }_{ 2 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{5x}{z+1}\text{, }&z\neq -1\\y\in \mathrm{C}\text{, }&x=0\text{ and }z=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5y-y\left(1-4z\right)=20x$$

Use the distributive property to multiply y by 1-4z.

$$5y-\left(y-4yz\right)=20x$$

To find the opposite of y-4yz, find the opposite of each term.

$$5y-y+4yz=20x$$

Combine 5y and -y to get 4y.

$$4y+4yz=20x$$

Combine all terms containing y.

$$\left(4+4z\right)y=20x$$

The equation is in standard form.

$$\left(4z+4\right)y=20x$$

Divide both sides by 4+4z.

$$\frac{\left(4z+4\right)y}{4z+4}=\frac{20x}{4z+4}$$

Dividing by 4+4z undoes the multiplication by 4+4z.

$$y=\frac{20x}{4z+4}$$

Divide 20x by 4+4z.

$$y=\frac{5x}{z+1}$$

Solve for x

$$x=\frac{y\left(z+1\right)}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5y-y\left(1-4z\right)=20x$$

Use the distributive property to multiply y by 1-4z.

$$5y-\left(y-4yz\right)=20x$$

To find the opposite of y-4yz, find the opposite of each term.

$$5y-y+4yz=20x$$

Combine 5y and -y to get 4y.

$$4y+4yz=20x$$

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

$$20x=4y+4yz$$

The equation is in standard form.

$$20x=4yz+4y$$

Divide both sides by 20.

$$\frac{20x}{20}=\frac{4y\left(z+1\right)}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$x=\frac{4y\left(z+1\right)}{20}$$

Divide 4y\left(1+z\right) by 20.

$$x=\frac{y\left(z+1\right)}{5}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{5x}{z+1}\text{, }&z\neq -1\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5y-y\left(1-4z\right)=20x$$

Use the distributive property to multiply y by 1-4z.

$$5y-\left(y-4yz\right)=20x$$

To find the opposite of y-4yz, find the opposite of each term.

$$5y-y+4yz=20x$$

Combine 5y and -y to get 4y.

$$4y+4yz=20x$$

Combine all terms containing y.

$$\left(4+4z\right)y=20x$$

The equation is in standard form.

$$\left(4z+4\right)y=20x$$

Divide both sides by 4+4z.

$$\frac{\left(4z+4\right)y}{4z+4}=\frac{20x}{4z+4}$$

Dividing by 4+4z undoes the multiplication by 4+4z.

$$y=\frac{20x}{4z+4}$$

Divide 20x by 4+4z.

$$y=\frac{5x}{z+1}$$