Solve y=8x+3/2x-6

$$y = \frac { 8 x + 3 } { 2 x - 6 }$$

Solve for x

$$x=\frac{3\left(2y+1\right)}{2\left(y-4\right)}$$

$$y\neq 4$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-3\right).

$$y\times 2\left(x-3\right)=8x+3$$

Use the distributive property to multiply y\times 2 by x-3.

$$2yx-3y\times 2=8x+3$$

Multiply -3 and 2 to get -6.

$$2yx-6y=8x+3$$

Subtract 8x from both sides.

$$2yx-6y-8x=3$$

Add 6y to both sides.

$$2yx-8x=3+6y$$

Combine all terms containing x.

$$\left(2y-8\right)x=3+6y$$

The equation is in standard form.

$$\left(2y-8\right)x=6y+3$$

Divide both sides by 2y-8.

$$\frac{\left(2y-8\right)x}{2y-8}=\frac{6y+3}{2y-8}$$

Dividing by 2y-8 undoes the multiplication by 2y-8.

$$x=\frac{6y+3}{2y-8}$$

Divide 3+6y by 2y-8.

$$x=\frac{3\left(2y+1\right)}{2\left(y-4\right)}$$

Variable x cannot be equal to 3.

$$x=\frac{3\left(2y+1\right)}{2\left(y-4\right)}\text{, }x\neq 3$$

Solve for y

$$y=\frac{8x+3}{2\left(x-3\right)}$$

$$x\neq 3$$