Solve y=3x-2/5x+1

$$y = \frac{ 3x-2 }{ 5x+1 }$$

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 5x+1.

$$y\left(5x+1\right)=3x-2$$

Use the distributive property to multiply y by 5x+1.

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

Subtract 3x from both sides.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 5y-3.

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

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

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

Divide -2-y by 5y-3.

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

Variable x cannot be equal to -\frac{1}{5}.

$$x=-\frac{y+2}{5y-3}\text{, }x\neq -\frac{1}{5}$$

Solve for y

$$y=-\frac{2-3x}{5x+1}$$

$$x\neq -\frac{1}{5}$$