Solve y=x-5/2x+1

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+1.

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

Use the distributive property to multiply y by 2x+1.

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

Subtract x from both sides.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2y-1.

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

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

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

Divide -5-y by 2y-1.

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

Variable x cannot be equal to -\frac{1}{2}.

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

Solve for y

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

$$x\neq -\frac{1}{2}$$