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

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

Solve for x_1

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

Steps for Solving Linear Equation

Add x_{2} to both sides.

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

Subtract 3x_{3} from both sides.

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

The equation is in standard form.

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

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Solve for x_2

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

Steps for Solving Linear Equation

Subtract 4x_{1} from both sides.

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

Subtract 3x_{3} from both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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