Solve -y=2x/3x-1

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3x-1.

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

Use the distributive property to multiply 3x-1 by y.

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

To find the opposite of 3xy-y, find the opposite of each term.

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

Subtract 2x from both sides.

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

Subtract y from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

Divide both sides by -3y-2.

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

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

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

Divide -y by -3y-2.

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

Variable x cannot be equal to \frac{1}{3}.

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

Solve for y

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

$$x\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x-1.

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

Use the distributive property to multiply 3x-1 by y.

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

To find the opposite of 3xy-y, find the opposite of each term.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -3x+1.

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

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

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