Solve 0-y/0-x=y-4/x-30

$$\frac{ 0-y }{ 0-x } = \frac{ y-4 }{ x-30 }$$

Solve for x

$$x=\frac{15y}{2}$$

$$y\neq 0\text{ and }y\neq 4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,30 since division by zero is not defined. Multiply both sides of the equation by x\left(x-30\right), the least common multiple of 0-x,x-30.

$$\left(-x+30\right)\left(0-y\right)=x\left(y-4\right)$$

Anything plus zero gives itself.

$$\left(-x+30\right)\left(-1\right)y=x\left(y-4\right)$$

Use the distributive property to multiply -x+30 by -1.

$$\left(x-30\right)y=x\left(y-4\right)$$

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

$$xy-30y=x\left(y-4\right)$$

Use the distributive property to multiply x by y-4.

$$xy-30y=xy-4x$$

Subtract xy from both sides.

$$xy-30y-xy=-4x$$

Combine xy and -xy to get 0.

$$-30y=-4x$$

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

$$-4x=-30y$$

Divide both sides by -4.

$$\frac{-4x}{-4}=-\frac{30y}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=-\frac{30y}{-4}$$

Divide -30y by -4.

$$x=\frac{15y}{2}$$

Variable x cannot be equal to any of the values 30,0.

$$x=\frac{15y}{2}\text{, }x\neq 30\text{ and }x\neq 0$$

Solve for y

$$y=\frac{2x}{15}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-30\right), the least common multiple of 0-x,x-30.

$$\left(-x+30\right)\left(0-y\right)=x\left(y-4\right)$$

Anything plus zero gives itself.

$$\left(-x+30\right)\left(-1\right)y=x\left(y-4\right)$$

Use the distributive property to multiply -x+30 by -1.

$$\left(x-30\right)y=x\left(y-4\right)$$

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

$$xy-30y=x\left(y-4\right)$$

Use the distributive property to multiply x by y-4.

$$xy-30y=xy-4x$$

Subtract xy from both sides.

$$xy-30y-xy=-4x$$

Combine xy and -xy to get 0.

$$-30y=-4x$$

Divide both sides by -30.

$$\frac{-30y}{-30}=-\frac{4x}{-30}$$

Dividing by -30 undoes the multiplication by -30.

$$y=-\frac{4x}{-30}$$

Divide -4x by -30.

$$y=\frac{2x}{15}$$