Solve -3000I_{3}-5000I_{3}+4000I_{4}-2000I_{3}+2000I_{2}-4000I_{3}+4000I_{1}=0

$$- 3000 I _ { 3 } - 5000 I _ { 3 } + 4000 I _ { 4 } - 2000 I _ { 3 } + 2000 I _ { 2 } - 4000 I _ { 3 } + 4000 I _ { 1 } = 0$$

Solve for I_1

$$I_{1}=\frac{7I_{3}}{2}-\frac{I_{2}}{2}-I_{4}$$

Steps for Solving Linear Equation

Combine -3000I_{3} and -5000I_{3} to get -8000I_{3}.

$$-8000I_{3}+4000I_{4}-2000I_{3}+2000I_{2}-4000I_{3}+4000I_{1}=0$$

Combine -8000I_{3} and -2000I_{3} to get -10000I_{3}.

$$-10000I_{3}+4000I_{4}+2000I_{2}-4000I_{3}+4000I_{1}=0$$

Combine -10000I_{3} and -4000I_{3} to get -14000I_{3}.

$$-14000I_{3}+4000I_{4}+2000I_{2}+4000I_{1}=0$$

Add 14000I_{3} to both sides. Anything plus zero gives itself.

$$4000I_{4}+2000I_{2}+4000I_{1}=14000I_{3}$$

Subtract 4000I_{4} from both sides.

$$2000I_{2}+4000I_{1}=14000I_{3}-4000I_{4}$$

Subtract 2000I_{2} from both sides.

$$4000I_{1}=14000I_{3}-4000I_{4}-2000I_{2}$$

The equation is in standard form.

$$4000I_{1}=-2000I_{2}+14000I_{3}-4000I_{4}$$

Divide both sides by 4000.

$$\frac{4000I_{1}}{4000}=\frac{-2000I_{2}+14000I_{3}-4000I_{4}}{4000}$$

Dividing by 4000 undoes the multiplication by 4000.

$$I_{1}=\frac{-2000I_{2}+14000I_{3}-4000I_{4}}{4000}$$

Divide 14000I_{3}-4000I_{4}-2000I_{2} by 4000.

$$I_{1}=\frac{7I_{3}}{2}-\frac{I_{2}}{2}-I_{4}$$

Solve for I_2

$$I_{2}=-2I_{1}+7I_{3}-2I_{4}$$

Steps for Solving Linear Equation

Combine -3000I_{3} and -5000I_{3} to get -8000I_{3}.

$$-8000I_{3}+4000I_{4}-2000I_{3}+2000I_{2}-4000I_{3}+4000I_{1}=0$$

Combine -8000I_{3} and -2000I_{3} to get -10000I_{3}.

$$-10000I_{3}+4000I_{4}+2000I_{2}-4000I_{3}+4000I_{1}=0$$

Combine -10000I_{3} and -4000I_{3} to get -14000I_{3}.

$$-14000I_{3}+4000I_{4}+2000I_{2}+4000I_{1}=0$$

Add 14000I_{3} to both sides. Anything plus zero gives itself.

$$4000I_{4}+2000I_{2}+4000I_{1}=14000I_{3}$$

Subtract 4000I_{4} from both sides.

$$2000I_{2}+4000I_{1}=14000I_{3}-4000I_{4}$$

Subtract 4000I_{1} from both sides.

$$2000I_{2}=14000I_{3}-4000I_{4}-4000I_{1}$$

The equation is in standard form.

$$2000I_{2}=-4000I_{1}+14000I_{3}-4000I_{4}$$

Divide both sides by 2000.

$$\frac{2000I_{2}}{2000}=\frac{-4000I_{1}+14000I_{3}-4000I_{4}}{2000}$$

Dividing by 2000 undoes the multiplication by 2000.

$$I_{2}=\frac{-4000I_{1}+14000I_{3}-4000I_{4}}{2000}$$

Divide 14000I_{3}-4000I_{4}-4000I_{1} by 2000.

$$I_{2}=-2I_{1}+7I_{3}-2I_{4}$$