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

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{5}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+5.

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

Use the distributive property to multiply y by 3x+5.

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

Subtract 2x from both sides.

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

Subtract 5y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 3y-2.

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

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

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

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

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

Variable x cannot be equal to -\frac{5}{3}.

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

Solve for y

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

$$x\neq -\frac{5}{3}$$