Solve -8x_{1}+2x_{2}-5x_{3}+6x_{4}=1

$$- 8 x _ { 1 } + 2 x _ { 2 } - 5 x _ { 3 } + 6 x _ { 4 } = 1$$

Solve for x_1

$$x_{1}=\frac{x_{2}}{4}+\frac{3x_{4}}{4}-\frac{5x_{3}}{8}-\frac{1}{8}$$

Steps for Solving Linear Equation

Subtract 2x_{2} from both sides.

$$-8x_{1}-5x_{3}+6x_{4}=1-2x_{2}$$

Add 5x_{3} to both sides.

$$-8x_{1}+6x_{4}=1-2x_{2}+5x_{3}$$

Subtract 6x_{4} from both sides.

$$-8x_{1}=1-2x_{2}+5x_{3}-6x_{4}$$

The equation is in standard form.

$$-8x_{1}=1-6x_{4}+5x_{3}-2x_{2}$$

Divide both sides by -8.

$$\frac{-8x_{1}}{-8}=\frac{1-6x_{4}+5x_{3}-2x_{2}}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x_{1}=\frac{1-6x_{4}+5x_{3}-2x_{2}}{-8}$$

Divide 1-2x_{2}+5x_{3}-6x_{4} by -8.

$$x_{1}=\frac{x_{2}}{4}+\frac{3x_{4}}{4}-\frac{5x_{3}}{8}-\frac{1}{8}$$

Solve for x_2

$$x_{2}=\frac{5x_{3}}{2}+4x_{1}-3x_{4}+\frac{1}{2}$$

Steps for Solving Linear Equation

Add 8x_{1} to both sides.

$$2x_{2}-5x_{3}+6x_{4}=1+8x_{1}$$

Add 5x_{3} to both sides.

$$2x_{2}+6x_{4}=1+8x_{1}+5x_{3}$$

Subtract 6x_{4} from both sides.

$$2x_{2}=1+8x_{1}+5x_{3}-6x_{4}$$

The equation is in standard form.

$$2x_{2}=8x_{1}+5x_{3}-6x_{4}+1$$

Divide both sides by 2.

$$\frac{2x_{2}}{2}=\frac{8x_{1}+5x_{3}-6x_{4}+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x_{2}=\frac{8x_{1}+5x_{3}-6x_{4}+1}{2}$$

Divide 1+8x_{1}+5x_{3}-6x_{4} by 2.

$$x_{2}=\frac{5x_{3}}{2}+4x_{1}-3x_{4}+\frac{1}{2}$$