Solve 2x_{1}+6x_{2}+4x_{3}=8

$$2 x _ { 1 } + 6 x _ { 2 } + 4 x _ { 3 } = 8$$

Solve for x_1

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

Steps for Solving Linear Equation

Subtract 6x_{2} from both sides.

$$2x_{1}+4x_{3}=8-6x_{2}$$

Subtract 4x_{3} from both sides.

$$2x_{1}=8-6x_{2}-4x_{3}$$

The equation is in standard form.

$$2x_{1}=8-4x_{3}-6x_{2}$$

Divide both sides by 2.

$$\frac{2x_{1}}{2}=\frac{8-4x_{3}-6x_{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x_{1}=\frac{8-4x_{3}-6x_{2}}{2}$$

Divide 8-6x_{2}-4x_{3} by 2.

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

Solve for x_2

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

Steps for Solving Linear Equation

Subtract 2x_{1} from both sides.

$$6x_{2}+4x_{3}=8-2x_{1}$$

Subtract 4x_{3} from both sides.

$$6x_{2}=8-2x_{1}-4x_{3}$$

The equation is in standard form.

$$6x_{2}=8-4x_{3}-2x_{1}$$

Divide both sides by 6.

$$\frac{6x_{2}}{6}=\frac{8-4x_{3}-2x_{1}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x_{2}=\frac{8-4x_{3}-2x_{1}}{6}$$

Divide 8-2x_{1}-4x_{3} by 6.

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