Solve x+y/10=x-y/30

$$\frac{ x+y }{ 10 } = \frac{ x-y }{ 30 }$$

Solve for x

$$x=-2y$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 10,30.

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

Use the distributive property to multiply 3 by x+y.

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

Subtract x from both sides.

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

Combine 3x and -x to get 2x.

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

Subtract 3y from both sides.

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

Combine -y and -3y to get -4y.

$$2x=-4y$$

Divide both sides by 2.

$$\frac{2x}{2}=-\frac{4y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=-\frac{4y}{2}$$

Divide -4y by 2.

$$x=-2y$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 10,30.

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

Use the distributive property to multiply 3 by x+y.

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

Add y to both sides.

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

Combine 3y and y to get 4y.

$$3x+4y=x$$

Subtract 3x from both sides.

$$4y=x-3x$$

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

$$4y=-2x$$

Divide both sides by 4.

$$\frac{4y}{4}=-\frac{2x}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=-\frac{2x}{4}$$

Divide -2x by 4.

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