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.

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

Add 5y to 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.

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

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

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

Solve for y

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

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