Solve 100x/100+x=y

$$\frac { 100 x } { 100 + x } = y$$

Solve for x

$$x=\frac{100y}{100-y}$$

$$y\neq 100$$

Steps for Solving Linear Equation

Variable x cannot be equal to -100 since division by zero is not defined. Multiply both sides of the equation by x+100.

$$100x=y\left(x+100\right)$$

Use the distributive property to multiply y by x+100.

$$100x=yx+100y$$

Subtract yx from both sides.

$$100x-yx=100y$$

Combine all terms containing x.

$$\left(100-y\right)x=100y$$

Divide both sides by -y+100.

$$\frac{\left(100-y\right)x}{100-y}=\frac{100y}{100-y}$$

Dividing by -y+100 undoes the multiplication by -y+100.

$$x=\frac{100y}{100-y}$$

Variable x cannot be equal to -100.

$$x=\frac{100y}{100-y}\text{, }x\neq -100$$

Solve for y

$$y=\frac{100x}{x+100}$$

$$x\neq -100$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+100.

$$100x=y\left(x+100\right)$$

Use the distributive property to multiply y by x+100.

$$100x=yx+100y$$

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

$$yx+100y=100x$$

Combine all terms containing y.

$$\left(x+100\right)y=100x$$

Divide both sides by 100+x.

$$\frac{\left(x+100\right)y}{x+100}=\frac{100x}{x+100}$$

Dividing by 100+x undoes the multiplication by 100+x.

$$y=\frac{100x}{x+100}$$