Solve x+6y/3x=y/x+1

$$\frac { x + 6 y } { 3 x } = \frac { y } { x } + 1$$

Solve for x

$$x=\frac{3y}{2}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3x,x.

$$x+6y=3y+3x$$

Subtract 3x from both sides.

$$x+6y-3x=3y$$

Combine x and -3x to get -2x.

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

Subtract 6y from both sides.

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

Combine 3y and -6y to get -3y.

$$-2x=-3y$$

Divide both sides by -2.

$$\frac{-2x}{-2}=-\frac{3y}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=-\frac{3y}{-2}$$

Divide -3y by -2.

$$x=\frac{3y}{2}$$

Variable x cannot be equal to 0.

$$x=\frac{3y}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{2x}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x, the least common multiple of 3x,x.

$$x+6y=3y+3x$$

Subtract 3y from both sides.

$$x+6y-3y=3x$$

Combine 6y and -3y to get 3y.

$$x+3y=3x$$

Subtract x from both sides.

$$3y=3x-x$$

Combine 3x and -x to get 2x.

$$3y=2x$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{2x}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{2x}{3}$$