Solve z=8x_{1}+4x_{2}

$$z = 8 x _ { 1 } + 4 x _ { 2 }$$

Solve for x_1

$$x_{1}=\frac{z-4x_{2}}{8}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$8x_{1}+4x_{2}=z$$

Subtract 4x_{2} from both sides.

$$8x_{1}=z-4x_{2}$$

Divide both sides by 8.

$$\frac{8x_{1}}{8}=\frac{z-4x_{2}}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x_{1}=\frac{z-4x_{2}}{8}$$

Divide z-4x_{2} by 8.

$$x_{1}=\frac{z}{8}-\frac{x_{2}}{2}$$

Solve for x_2

$$x_{2}=\frac{z-8x_{1}}{4}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$8x_{1}+4x_{2}=z$$

Subtract 8x_{1} from both sides.

$$4x_{2}=z-8x_{1}$$

Divide both sides by 4.

$$\frac{4x_{2}}{4}=\frac{z-8x_{1}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x_{2}=\frac{z-8x_{1}}{4}$$

Divide z-8x_{1} by 4.

$$x_{2}=\frac{z}{4}-2x_{1}$$