Solve y^-1=-x+8/3

$${ y }^{ -1 } = \frac{ -x+8 }{ 3 }$$

Solve for x

$$x=8-\frac{3}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3y^{-1}=-x+8$$

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

$$-x+8=3y^{-1}$$

Subtract 8 from both sides.

$$-x=3y^{-1}-8$$

Reorder the terms.

$$-x=-8+3\times \frac{1}{y}$$

Multiply both sides of the equation by y.

$$-xy=y\left(-8\right)+3\times 1$$

Multiply 3 and 1 to get 3.

$$-xy=y\left(-8\right)+3$$

The equation is in standard form.

$$\left(-y\right)x=3-8y$$

Divide both sides by -y.

$$\frac{\left(-y\right)x}{-y}=\frac{3-8y}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$x=\frac{3-8y}{-y}$$

Divide -8y+3 by -y.

$$x=8-\frac{3}{y}$$

Solve for y

$$y=-\frac{3}{x-8}$$

$$x\neq 8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3y^{-1}=-x+8$$

Reorder the terms.

$$3\times \frac{1}{y}=8-x$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$3\times 1=y\times 8-xy$$

Multiply 3 and 1 to get 3.

$$3=y\times 8-xy$$

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

$$y\times 8-xy=3$$

Combine all terms containing y.

$$\left(8-x\right)y=3$$

Divide both sides by 8-x.

$$\frac{\left(8-x\right)y}{8-x}=\frac{3}{8-x}$$

Dividing by 8-x undoes the multiplication by 8-x.

$$y=\frac{3}{8-x}$$

Variable y cannot be equal to 0.

$$y=\frac{3}{8-x}\text{, }y\neq 0$$