Solve 6x-1/y-3=2

$$\frac { 6 x - 1 } { y } - 3 = 2$$

Solve for x

$$x=\frac{5y+1}{6}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$6x-1+y\left(-3\right)=2y$$

Add 1 to both sides.

$$6x+y\left(-3\right)=2y+1$$

Subtract y\left(-3\right) from both sides.

$$6x=2y+1-y\left(-3\right)$$

Combine 2y and -y\left(-3\right) to get 5y.

$$6x=5y+1$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{5y+1}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{5y+1}{6}$$

Solve for y

$$y=\frac{6x-1}{5}$$

$$x\neq \frac{1}{6}$$

Steps for Solving Linear Equation

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

$$6x-1+y\left(-3\right)=2y$$

Subtract 2y from both sides.

$$6x-1+y\left(-3\right)-2y=0$$

Combine y\left(-3\right) and -2y to get -5y.

$$6x-1-5y=0$$

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$-1-5y=-6x$$

Add 1 to both sides.

$$-5y=-6x+1$$

The equation is in standard form.

$$-5y=1-6x$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{1-6x}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{1-6x}{-5}$$

Divide -6x+1 by -5.

$$y=\frac{6x-1}{5}$$

Variable y cannot be equal to 0.

$$y=\frac{6x-1}{5}\text{, }y\neq 0$$