Solve xy+xz+yz=19

$$xy+xz+yz=19$$

Solve for x

$$x=-\frac{yz-19}{y+z}$$

$$y\neq -z$$

Steps for Solving Linear Equation

Subtract yz from both sides.

$$xy+xz=19-yz$$

Combine all terms containing x.

$$\left(y+z\right)x=19-yz$$

Divide both sides by y+z.

$$\frac{\left(y+z\right)x}{y+z}=\frac{19-yz}{y+z}$$

Dividing by y+z undoes the multiplication by y+z.

$$x=\frac{19-yz}{y+z}$$

Solve for y

$$y=-\frac{xz-19}{x+z}$$

$$x\neq -z$$

Steps for Solving Linear Equation

Subtract xz from both sides.

$$xy+yz=19-xz$$

Combine all terms containing y.

$$\left(x+z\right)y=19-xz$$

Divide both sides by x+z.

$$\frac{\left(x+z\right)y}{x+z}=\frac{19-xz}{x+z}$$

Dividing by x+z undoes the multiplication by x+z.

$$y=\frac{19-xz}{x+z}$$