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

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

Solve for x_1

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

Steps for Solving Linear Equation

Subtract 2x_{2} from both sides.

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

Add x_{3} to both sides.

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

The equation is in standard form.

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Solve for x_2

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

Steps for Solving Linear Equation

Subtract 3x_{1} from both sides.

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

Add x_{3} to both sides.

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

The equation is in standard form.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

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

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