Determine the values of I1, I2, and I3 that satisfy the following three equations. -1.02 I1 + I2 + I3 = 5.45, and -3.12 I1 + I2 =0 and 1.35 I1 + 1.35 I3 =0

102-i1-i2-i3-545

#1

Determine the values of I1, I2, and I3 that satisfy the following three equations.
-1.02 I1 + I2 + I3 = 5.45, and -3.12 I1 + I2 =0 and 1.35 I1 + 1.35 I3 =0

Answer:

-3.12 (I1) + I2 = 0
3.12 (I1) = I2 – EQUATION 1

1.35(I1) + 1.35(I3) = 0
-I1 = I3 – EQUATION 2

-1.02I1 + I2 + I3 = 5.45
PLUG THE PREVIOUS TWO EQUATIONS FOR I2 AND I3

-1.02(I1) + (3.12(I1)) + (-(I1)) = 5.45

1.1(I1) = 5.45
I1 = 4.954

SOLVE THE REST

-I1 = I3
-4.954 = I3

3.12 (I1) = I2

3.12(4.954) = I2

I2 = 15.45

CHECK

-1.02(4.954) + 15.45 + (-4.954) = 5.45
INDEED IT EQUALS 5.45 WIT A BIT OF ROUNDING ERROR