Solve y=4-6x/x-1

$$y = \frac { 4 - 6 x } { x - 1 }$$

Solve for x

$$x=\frac{y+4}{y+6}$$

$$y\neq -6$$

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.

$$y\left(x-1\right)=4-6x$$

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

$$yx-y=4-6x$$

Add 6x to both sides.

$$yx-y+6x=4$$

Add y to both sides.

$$yx+6x=4+y$$

Combine all terms containing x.

$$\left(y+6\right)x=4+y$$

The equation is in standard form.

$$\left(y+6\right)x=y+4$$

Divide both sides by y+6.

$$\frac{\left(y+6\right)x}{y+6}=\frac{y+4}{y+6}$$

Dividing by y+6 undoes the multiplication by y+6.

$$x=\frac{y+4}{y+6}$$

Variable x cannot be equal to 1.

$$x=\frac{y+4}{y+6}\text{, }x\neq 1$$

Solve for y

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

$$x\neq 1$$