Solve y=4-6x/3x-9

$$y = \frac { 4 - 6 x } { 3 x - 9 }$$

Solve for x

$$x=\frac{9y+4}{3\left(y+2\right)}$$

$$y\neq -2$$

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 3\left(x-3\right).

$$y\times 3\left(x-3\right)=4-6x$$

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

$$3yx-3y\times 3=4-6x$$

Multiply -3 and 3 to get -9.

$$3yx-9y=4-6x$$

Add 6x to both sides.

$$3yx-9y+6x=4$$

Add 9y to both sides.

$$3yx+6x=4+9y$$

Combine all terms containing x.

$$\left(3y+6\right)x=4+9y$$

The equation is in standard form.

$$\left(3y+6\right)x=9y+4$$

Divide both sides by 3y+6.

$$\frac{\left(3y+6\right)x}{3y+6}=\frac{9y+4}{3y+6}$$

Dividing by 3y+6 undoes the multiplication by 3y+6.

$$x=\frac{9y+4}{3y+6}$$

Divide 9y+4 by 3y+6.

$$x=\frac{9y+4}{3\left(y+2\right)}$$

Variable x cannot be equal to 3.

$$x=\frac{9y+4}{3\left(y+2\right)}\text{, }x\neq 3$$

Solve for y

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

$$x\neq 3$$