Solve 3x_{1}-6x_{2}-x_{3}=25

$$3 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 25$$

Solve for x_1

$$x_{1}=\frac{6x_{2}+x_{3}+25}{3}$$

Steps for Solving Linear Equation

Add 6x_{2} to both sides.

$$3x_{1}-x_{3}=25+6x_{2}$$

Add x_{3} to both sides.

$$3x_{1}=25+6x_{2}+x_{3}$$

The equation is in standard form.

$$3x_{1}=6x_{2}+x_{3}+25$$

Divide both sides by 3.

$$\frac{3x_{1}}{3}=\frac{6x_{2}+x_{3}+25}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x_{1}=\frac{6x_{2}+x_{3}+25}{3}$$

Divide 25+6x_{2}+x_{3} by 3.

$$x_{1}=\frac{x_{3}}{3}+2x_{2}+\frac{25}{3}$$

Solve for x_2

$$x_{2}=\frac{x_{1}}{2}-\frac{x_{3}}{6}-\frac{25}{6}$$

Steps for Solving Linear Equation

Subtract 3x_{1} from both sides.

$$-6x_{2}-x_{3}=25-3x_{1}$$

Add x_{3} to both sides.

$$-6x_{2}=25-3x_{1}+x_{3}$$

The equation is in standard form.

$$-6x_{2}=25+x_{3}-3x_{1}$$

Divide both sides by -6.

$$\frac{-6x_{2}}{-6}=\frac{25+x_{3}-3x_{1}}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x_{2}=\frac{25+x_{3}-3x_{1}}{-6}$$

Divide 25-3x_{1}+x_{3} by -6.

$$x_{2}=\frac{x_{1}}{2}-\frac{x_{3}}{6}-\frac{25}{6}$$