Solve x=5-2y/y-1+3

$$x = \frac { 5 - 2 y } { y - 1 } + 3$$

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by y-1.

$$x\left(y-1\right)=5-2y+\left(y-1\right)\times 3$$

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

$$xy-x=5-2y+\left(y-1\right)\times 3$$

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

$$xy-x=5-2y+3y-3$$

Combine -2y and 3y to get y.

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

Subtract 3 from 5 to get 2.

$$xy-x=2+y$$

Subtract y from both sides.

$$xy-x-y=2$$

Add x to both sides.

$$xy-y=2+x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

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

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

Variable y cannot be equal to 1.

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

Solve for x

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

$$y\neq 1$$