Solve y=3x/2x-3

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

Solve for x

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

$$y\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-3.

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

Use the distributive property to multiply y by 2x-3.

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

Subtract 3x from both sides.

$$2yx-3y-3x=0$$

Add 3y to both sides. Anything plus zero gives itself.

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

Combine all terms containing x.

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

Divide both sides by 2y-3.

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

Dividing by 2y-3 undoes the multiplication by 2y-3.

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

Variable x cannot be equal to \frac{3}{2}.

$$x=\frac{3y}{2y-3}\text{, }x\neq \frac{3}{2}$$

Solve for y

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

$$x\neq \frac{3}{2}$$