Solve y=5x+1/2x-4

$$y = \frac { 5 x + 1 } { 2 x - 4 }$$

Solve for x

$$x=\frac{4y+1}{2y-5}$$

$$y\neq \frac{5}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right).

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

Use the distributive property to multiply y\times 2 by x-2.

$$2yx-2y\times 2=5x+1$$

Multiply -2 and 2 to get -4.

$$2yx-4y=5x+1$$

Subtract 5x from both sides.

$$2yx-4y-5x=1$$

Add 4y to both sides.

$$2yx-5x=1+4y$$

Combine all terms containing x.

$$\left(2y-5\right)x=1+4y$$

The equation is in standard form.

$$\left(2y-5\right)x=4y+1$$

Divide both sides by 2y-5.

$$\frac{\left(2y-5\right)x}{2y-5}=\frac{4y+1}{2y-5}$$

Dividing by 2y-5 undoes the multiplication by 2y-5.

$$x=\frac{4y+1}{2y-5}$$

Variable x cannot be equal to 2.

$$x=\frac{4y+1}{2y-5}\text{, }x\neq 2$$

Solve for y

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

$$x\neq 2$$