Solve 4x_{1}+2x_{2}+x_{3}=4

$$4 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } = 4$$

Solve for x_1

$$x_{1}=-\frac{x_{2}}{2}-\frac{x_{3}}{4}+1$$

Steps for Solving Linear Equation

Subtract 2x_{2} from both sides.

$$4x_{1}+x_{3}=4-2x_{2}$$

Subtract x_{3} from both sides.

$$4x_{1}=4-2x_{2}-x_{3}$$

The equation is in standard form.

$$4x_{1}=4-x_{3}-2x_{2}$$

Divide both sides by 4.

$$\frac{4x_{1}}{4}=\frac{4-x_{3}-2x_{2}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x_{1}=\frac{4-x_{3}-2x_{2}}{4}$$

Divide 4-2x_{2}-x_{3} by 4.

$$x_{1}=-\frac{x_{2}}{2}-\frac{x_{3}}{4}+1$$

Solve for x_2

$$x_{2}=-\frac{x_{3}}{2}-2x_{1}+2$$

Steps for Solving Linear Equation

Subtract 4x_{1} from both sides.

$$2x_{2}+x_{3}=4-4x_{1}$$

Subtract x_{3} from both sides.

$$2x_{2}=4-4x_{1}-x_{3}$$

The equation is in standard form.

$$2x_{2}=4-x_{3}-4x_{1}$$

Divide both sides by 2.

$$\frac{2x_{2}}{2}=\frac{4-x_{3}-4x_{1}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x_{2}=\frac{4-x_{3}-4x_{1}}{2}$$

Divide 4-4x_{1}-x_{3} by 2.

$$x_{2}=-\frac{x_{3}}{2}-2x_{1}+2$$