Solve x/100=x-30/y-1000

$$\frac { x } { 100 } = \frac { x - 30 } { y - 1000 }$$

Solve for x

$$x=-\frac{3000}{y-1100}$$

$$y\neq 1100\text{ and }y\neq 1000$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100\left(y-1000\right), the least common multiple of 100,y-1000.

$$\left(y-1000\right)x=100\left(x-30\right)$$

Use the distributive property to multiply y-1000 by x.

$$yx-1000x=100\left(x-30\right)$$

Use the distributive property to multiply 100 by x-30.

$$yx-1000x=100x-3000$$

Subtract 100x from both sides.

$$yx-1000x-100x=-3000$$

Combine -1000x and -100x to get -1100x.

$$yx-1100x=-3000$$

Combine all terms containing x.

$$\left(y-1100\right)x=-3000$$

Divide both sides by y-1100.

$$\frac{\left(y-1100\right)x}{y-1100}=-\frac{3000}{y-1100}$$

Dividing by y-1100 undoes the multiplication by y-1100.

$$x=-\frac{3000}{y-1100}$$

Solve for y

$$y=1100-\frac{3000}{x}$$

$$x\neq 30\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1000 since division by zero is not defined. Multiply both sides of the equation by 100\left(y-1000\right), the least common multiple of 100,y-1000.

$$\left(y-1000\right)x=100\left(x-30\right)$$

Use the distributive property to multiply y-1000 by x.

$$yx-1000x=100\left(x-30\right)$$

Use the distributive property to multiply 100 by x-30.

$$yx-1000x=100x-3000$$

Add 1000x to both sides.

$$yx=100x-3000+1000x$$

Combine 100x and 1000x to get 1100x.

$$yx=1100x-3000$$

The equation is in standard form.

$$xy=1100x-3000$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{1100x-3000}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{1100x-3000}{x}$$

Divide 1100x-3000 by x.

$$y=1100-\frac{3000}{x}$$

Variable y cannot be equal to 1000.

$$y=1100-\frac{3000}{x}\text{, }y\neq 1000$$