Solve y=2x-5/x-1

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

Solve for x

$$x=-\frac{5-y}{y-2}$$

$$y\neq 2$$

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.

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

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

$$yx-y=2x-5$$

Subtract 2x from both sides.

$$yx-y-2x=-5$$

Add y to both sides.

$$yx-2x=-5+y$$

Combine all terms containing x.

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

The equation is in standard form.

$$\left(y-2\right)x=y-5$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{y-5}{y-2}$$

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

$$x=\frac{y-5}{y-2}$$

Variable x cannot be equal to 1.

$$x=\frac{y-5}{y-2}\text{, }x\neq 1$$

Solve for y

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

$$x\neq 1$$