Solve 1/x+5=y

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

Solve for x

$$x=-\frac{1}{5-y}$$

$$y\neq 5$$

Steps for Solving Linear Equation

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

$$1+x\times 5=yx$$

Subtract yx from both sides.

$$1+x\times 5-yx=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$x\times 5-yx=-1$$

Combine all terms containing x.

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

Divide both sides by 5-y.

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

Dividing by 5-y undoes the multiplication by 5-y.

$$x=-\frac{1}{5-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{1}{5-y}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1+x\times 5=yx$$

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

$$yx=1+x\times 5$$

The equation is in standard form.

$$xy=5x+1$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{5x+1}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide 5x+1 by x.

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