Solve (100-x)y(1+0.02x)=100x

$$(100-x)y(1+0.02x)=100x$$

Solve for y

$$y=-\frac{5000x}{\left(x-100\right)\left(x+50\right)}$$

$$x\neq -50\text{ and }x\neq 100$$

Steps for Solving Linear Equation

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

$$\left(100y-xy\right)\left(1+0.02x\right)=100x$$

Use the distributive property to multiply 100y-xy by 1+0.02x and combine like terms.

$$100y+yx-0.02x^{2}y=100x$$

Combine all terms containing y.

$$\left(100+x-0.02x^{2}\right)y=100x$$

The equation is in standard form.

$$\left(-\frac{x^{2}}{50}+x+100\right)y=100x$$

Divide both sides by 100+x-0.02x^{2}.

$$\frac{\left(-\frac{x^{2}}{50}+x+100\right)y}{-\frac{x^{2}}{50}+x+100}=\frac{100x}{-\frac{x^{2}}{50}+x+100}$$

Dividing by 100+x-0.02x^{2} undoes the multiplication by 100+x-0.02x^{2}.

$$y=\frac{100x}{-\frac{x^{2}}{50}+x+100}$$

Divide 100x by 100+x-0.02x^{2}.

$$y=-\frac{5000x}{\left(x-100\right)\left(x+50\right)}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{25\left(\sqrt{9y^{2}-200y+10000}-y+100\right)}{y}\text{; }x=-\frac{25\left(-\sqrt{9y^{2}-200y+10000}-y+100\right)}{y}\text{, }&y\neq 0\end{matrix}\right.$$