Solve 3(x+y)+2/y=3x+2

$$\frac{ 3(x+y)+2 }{ y } =3x+2$$

Solve for x

$$x=-\frac{y+2}{3\left(1-y\right)}$$

$$y\neq 1\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$3\left(x+y\right)+2=3xy+y\times 2$$

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

$$3x+3y+2=3xy+y\times 2$$

Subtract 3xy from both sides.

$$3x+3y+2-3xy=y\times 2$$

Subtract 3y from both sides.

$$3x+2-3xy=y\times 2-3y$$

Combine y\times 2 and -3y to get -y.

$$3x+2-3xy=-y$$

Subtract 2 from both sides.

$$3x-3xy=-y-2$$

Combine all terms containing x.

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

Divide both sides by -3y+3.

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

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

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

Divide -y-2 by -3y+3.

$$x=-\frac{y+2}{3\left(1-y\right)}$$

Solve for y

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

$$x\neq -\frac{2}{3}\text{ and }x\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$3\left(x+y\right)+2=3xy+y\times 2$$

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

$$3x+3y+2=3xy+y\times 2$$

Subtract 3xy from both sides.

$$3x+3y+2-3xy=y\times 2$$

Subtract y\times 2 from both sides.

$$3x+3y+2-3xy-y\times 2=0$$

Combine 3y and -y\times 2 to get y.

$$3x+y+2-3xy=0$$

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$y+2-3xy=-3x$$

Subtract 2 from both sides.

$$y-3xy=-3x-2$$

Combine all terms containing y.

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

Divide both sides by 1-3x.

$$\frac{\left(1-3x\right)y}{1-3x}=\frac{-3x-2}{1-3x}$$

Dividing by 1-3x undoes the multiplication by 1-3x.

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

Divide -3x-2 by 1-3x.

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

Variable y cannot be equal to 0.

$$y=-\frac{3x+2}{1-3x}\text{, }y\neq 0$$