Solve 10y+x-18=10x+y

$$10y+x-18=10x+y$$

Solve for x

$$x=y-2$$

Steps for Solving Linear Equation

Subtract 10x from both sides.

$$10y+x-18-10x=y$$

Combine x and -10x to get -9x.

$$10y-9x-18=y$$

Subtract 10y from both sides.

$$-9x-18=y-10y$$

Combine y and -10y to get -9y.

$$-9x-18=-9y$$

Add 18 to both sides.

$$-9x=-9y+18$$

The equation is in standard form.

$$-9x=18-9y$$

Divide both sides by -9.

$$\frac{-9x}{-9}=\frac{18-9y}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$x=\frac{18-9y}{-9}$$

Divide -9y+18 by -9.

$$x=y-2$$

Solve for y

$$y=x+2$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$10y+x-18-y=10x$$

Combine 10y and -y to get 9y.

$$9y+x-18=10x$$

Subtract x from both sides.

$$9y-18=10x-x$$

Combine 10x and -x to get 9x.

$$9y-18=9x$$

Add 18 to both sides.

$$9y=9x+18$$

Divide both sides by 9.

$$\frac{9y}{9}=\frac{9x+18}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$y=\frac{9x+18}{9}$$

Divide 18+9x by 9.

$$y=x+2$$