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

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

Solve for x

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

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

Steps for Solving Linear Equation

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

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

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

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

Subtract 3x from both sides.

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

Subtract 3y from both sides.

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

Combine all terms containing x.

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

Divide both sides by 5y-3.

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

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

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

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

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

Solve for y

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

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