Solve 10x+x+10y+y+10z+z=100x+10y+z

$$10x+x+10y+y+10z+z=100x+10y+z$$

Solve for x

$$x=\frac{y+10z}{89}$$

Steps for Solving Linear Equation

Combine 10x and x to get 11x.

$$11x+10y+y+10z+z=100x+10y+z$$

Combine 10y and y to get 11y.

$$11x+11y+10z+z=100x+10y+z$$

Combine 10z and z to get 11z.

$$11x+11y+11z=100x+10y+z$$

Subtract 100x from both sides.

$$11x+11y+11z-100x=10y+z$$

Combine 11x and -100x to get -89x.

$$-89x+11y+11z=10y+z$$

Subtract 11y from both sides.

$$-89x+11z=10y+z-11y$$

Combine 10y and -11y to get -y.

$$-89x+11z=-y+z$$

Subtract 11z from both sides.

$$-89x=-y+z-11z$$

Combine z and -11z to get -10z.

$$-89x=-y-10z$$

Divide both sides by -89.

$$\frac{-89x}{-89}=\frac{-y-10z}{-89}$$

Dividing by -89 undoes the multiplication by -89.

$$x=\frac{-y-10z}{-89}$$

Divide -y-10z by -89.

$$x=\frac{y+10z}{89}$$

Solve for y

$$y=89x-10z$$

Solution Steps

Combine 10x and x to get 11x.

$$11x+10y+y+10z+z=100x+10y+z$$

Combine 10y and y to get 11y.

$$11x+11y+10z+z=100x+10y+z$$

Combine 10z and z to get 11z.

$$11x+11y+11z=100x+10y+z$$

Subtract 10y from both sides.

$$11x+11y+11z-10y=100x+z$$

Combine 11y and -10y to get y.

$$11x+y+11z=100x+z$$

Subtract 11x from both sides.

$$y+11z=100x+z-11x$$

Combine 100x and -11x to get 89x.

$$y+11z=89x+z$$

Subtract 11z from both sides.

$$y=89x+z-11z$$

Combine z and -11z to get -10z.

$$y=89x-10z$$