Solve 1=2y-1/3-x

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

Solve for x

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

$$y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 2y by -x+3.

$$-x+3=-2xy+6y-1$$

Add 2xy to both sides.

$$-x+3+2xy=6y-1$$

Subtract 3 from both sides.

$$-x+2xy=6y-1-3$$

Subtract 3 from -1 to get -4.

$$-x+2xy=6y-4$$

Combine all terms containing x.

$$\left(-1+2y\right)x=6y-4$$

The equation is in standard form.

$$\left(2y-1\right)x=6y-4$$

Divide both sides by -1+2y.

$$\frac{\left(2y-1\right)x}{2y-1}=\frac{6y-4}{2y-1}$$

Dividing by -1+2y undoes the multiplication by -1+2y.

$$x=\frac{6y-4}{2y-1}$$

Divide -4+6y by -1+2y.

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

Variable x cannot be equal to 3.

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

Solve for y

$$y=-\frac{4-x}{2\left(x-3\right)}$$

$$x\neq 3$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 2y by -x+3.

$$-x+3=-2xy+6y-1$$

Swap sides so that all variable terms are on the left hand side.

$$-2xy+6y-1=-x+3$$

Add 1 to both sides.

$$-2xy+6y=-x+3+1$$

Add 3 and 1 to get 4.

$$-2xy+6y=-x+4$$

Combine all terms containing y.

$$\left(-2x+6\right)y=-x+4$$

The equation is in standard form.

$$\left(6-2x\right)y=4-x$$

Divide both sides by -2x+6.

$$\frac{\left(6-2x\right)y}{6-2x}=\frac{4-x}{6-2x}$$

Dividing by -2x+6 undoes the multiplication by -2x+6.

$$y=\frac{4-x}{6-2x}$$

Divide -x+4 by -2x+6.

$$y=\frac{4-x}{2\left(3-x\right)}$$