Solve x-1/y=1/3

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3y, the least common multiple of y,3.

$$3\left(x-1\right)=y$$

Use the distributive property to multiply 3 by x-1.

$$3x-3=y$$

Add 3 to both sides.

$$3x=y+3$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Divide y+3 by 3.

$$x=\frac{y}{3}+1$$

Solve for y

$$y=3\left(x-1\right)$$

$$x\neq 1$$

Solution Steps

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

$$3\left(x-1\right)=y$$

Use the distributive property to multiply 3 by x-1.

$$3x-3=y$$

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

$$y=3x-3$$

Variable y cannot be equal to 0.

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