Solve y=3x-2/5x-6

$$y = \frac { 3 x - 2 } { 5 x - 6 }$$

Solve for x

$$x=-\frac{2\left(1-3y\right)}{5y-3}$$

$$y\neq \frac{3}{5}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{6}{5} since division by zero is not defined. Multiply both sides of the equation by 5x-6.

$$y\left(5x-6\right)=3x-2$$

Use the distributive property to multiply y by 5x-6.

$$5yx-6y=3x-2$$

Subtract 3x from both sides.

$$5yx-6y-3x=-2$$

Add 6y to both sides.

$$5yx-3x=-2+6y$$

Combine all terms containing x.

$$\left(5y-3\right)x=-2+6y$$

The equation is in standard form.

$$\left(5y-3\right)x=6y-2$$

Divide both sides by 5y-3.

$$\frac{\left(5y-3\right)x}{5y-3}=\frac{6y-2}{5y-3}$$

Dividing by 5y-3 undoes the multiplication by 5y-3.

$$x=\frac{6y-2}{5y-3}$$

Divide -2+6y by 5y-3.

$$x=\frac{2\left(3y-1\right)}{5y-3}$$

Variable x cannot be equal to \frac{6}{5}.

$$x=\frac{2\left(3y-1\right)}{5y-3}\text{, }x\neq \frac{6}{5}$$

Solve for y

$$y=-\frac{2-3x}{5x-6}$$

$$x\neq \frac{6}{5}$$