Solve 10.5I_{1}+9I_{2}+6I_{3}=12

$$10.5 I _ { 1 } + 9 I _ { 2 } + 6 I _ { 3 } = 12$$

Solve for I_1

$$I_{1}=\frac{8-4I_{3}-6I_{2}}{7}$$

Steps for Solving Linear Equation

Subtract 9I_{2} from both sides.

$$10.5I_{1}+6I_{3}=12-9I_{2}$$

Subtract 6I_{3} from both sides.

$$10.5I_{1}=12-9I_{2}-6I_{3}$$

The equation is in standard form.

$$10.5I_{1}=12-6I_{3}-9I_{2}$$

Divide both sides of the equation by 10.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{10.5I_{1}}{10.5}=\frac{12-6I_{3}-9I_{2}}{10.5}$$

Dividing by 10.5 undoes the multiplication by 10.5.

$$I_{1}=\frac{12-6I_{3}-9I_{2}}{10.5}$$

Divide 12-9I_{2}-6I_{3} by 10.5 by multiplying 12-9I_{2}-6I_{3} by the reciprocal of 10.5.

$$I_{1}=\frac{8-4I_{3}-6I_{2}}{7}$$

Solve for I_2

$$I_{2}=-\frac{2I_{3}}{3}-\frac{7I_{1}}{6}+\frac{4}{3}$$

Steps for Solving Linear Equation

Subtract 10.5I_{1} from both sides.

$$9I_{2}+6I_{3}=12-10.5I_{1}$$

Subtract 6I_{3} from both sides.

$$9I_{2}=12-10.5I_{1}-6I_{3}$$

The equation is in standard form.

$$9I_{2}=-\frac{21I_{1}}{2}-6I_{3}+12$$

Divide both sides by 9.

$$\frac{9I_{2}}{9}=\frac{-\frac{21I_{1}}{2}-6I_{3}+12}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$I_{2}=\frac{-\frac{21I_{1}}{2}-6I_{3}+12}{9}$$

Divide 12-\frac{21I_{1}}{2}-6I_{3} by 9.

$$I_{2}=-\frac{2I_{3}}{3}-\frac{7I_{1}}{6}+\frac{4}{3}$$