Solve y=2x-1/x-1quad(4)

$$y = \frac { 2 x - 1 } { x - 1 } \quad ( 4 )$$

Solve for x

$$x=-\frac{y-4}{8-y}$$

$$y\neq 8$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply 2x-1 by 4.

$$yx-y=8x-4$$

Subtract 8x from both sides.

$$yx-y-8x=-4$$

Add y to both sides.

$$yx-8x=-4+y$$

Combine all terms containing x.

$$\left(y-8\right)x=-4+y$$

The equation is in standard form.

$$\left(y-8\right)x=y-4$$

Divide both sides by y-8.

$$\frac{\left(y-8\right)x}{y-8}=\frac{y-4}{y-8}$$

Dividing by y-8 undoes the multiplication by y-8.

$$x=\frac{y-4}{y-8}$$

Variable x cannot be equal to 1.

$$x=\frac{y-4}{y-8}\text{, }x\neq 1$$

Solve for y

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

$$x\neq 1$$