Solve 100x+120y=100y+120x+200

$$100 x + 120 y = 100 y + 120 x + 200$$

Solve for x

$$x=y-10$$

Steps for Solving Linear Equation

Subtract 120x from both sides.

$$100x+120y-120x=100y+200$$

Combine 100x and -120x to get -20x.

$$-20x+120y=100y+200$$

Subtract 120y from both sides.

$$-20x=100y+200-120y$$

Combine 100y and -120y to get -20y.

$$-20x=-20y+200$$

The equation is in standard form.

$$-20x=200-20y$$

Divide both sides by -20.

$$\frac{-20x}{-20}=\frac{200-20y}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$x=\frac{200-20y}{-20}$$

Divide -20y+200 by -20.

$$x=y-10$$

Solve for y

$$y=x+10$$

Steps for Solving Linear Equation

Subtract 100y from both sides.

$$100x+120y-100y=120x+200$$

Combine 120y and -100y to get 20y.

$$100x+20y=120x+200$$

Subtract 100x from both sides.

$$20y=120x+200-100x$$

Combine 120x and -100x to get 20x.

$$20y=20x+200$$

Divide both sides by 20.

$$\frac{20y}{20}=\frac{20x+200}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$y=\frac{20x+200}{20}$$

Divide 200+20x by 20.

$$y=x+10$$