Solve y-6/x-0=1/3

$$\frac { y - 6 } { x - 0 } = \frac { 1 } { 3 }$$

Solve for x

$$x=3\left(y-6\right)$$

$$y\neq 6$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x-0,3.

$$3\left(y-6\right)=x$$

Use the distributive property to multiply 3 by y-6.

$$3y-18=x$$

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

$$x=3y-18$$

Variable x cannot be equal to 0.

$$x=3y-18\text{, }x\neq 0$$

Solve for y

$$y=\frac{x+18}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x, the least common multiple of x-0,3.

$$3\left(y-6\right)=x$$

Use the distributive property to multiply 3 by y-6.

$$3y-18=x$$

Add 18 to both sides.

$$3y=x+18$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{x+18}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{x+18}{3}$$

Divide x+18 by 3.

$$y=\frac{x}{3}+6$$