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

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-5.

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

Use the distributive property to multiply y by 2x-5.

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

Subtract 3x from both sides.

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

Add 5y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2y-3.

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

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

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

Variable x cannot be equal to \frac{5}{2}.

$$x=\frac{5y-2}{2y-3}\text{, }x\neq \frac{5}{2}$$

Solve for y

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

$$x\neq \frac{5}{2}$$