Solve for I1 and I2 in the following equation: 100I1 + 30I2 = 30
75I1 - 45I2 = 20
A) I1 = 28.9 mA, I2 = 3.7 mA
B) I1 = 0.289 A, I2 = 0.037 A
C) I1 = 0.037 A, I2 = 0.368 A
D) I1 = 0.289 A, I2 = -0.037 A

Question

Quizplus · Accepted Answer

To solve for I1 and I2, we can use the method of simultaneous equations. First, we can multiply the second equation by 2/3 to make the coefficients of I2 in both equations equal in magnitude but opposite in sign:$$100I1 + 30I2 = 30$$$$50I1 - 30I2 = \frac{2}{3} \times 20 = 13.\overline{3}$$Adding these equations to eliminate I2 gives:$$150I1 = 43.\overline{3}$$$$I1 = \frac{43.\overline{3}}{150} = 0.289 A$$Substituting I1 = 0.289 A into the first original equation:$$100(0.289) + 30I2 = 30$$$$28.9 + 30I2 = 30$$$$30I2 = 1.1$$$$I2 = \frac{1.1}{30} = 0.036\overline{6} A \approx 0.037 A$$Therefore, I1 = 0.289 A and I2 = 0.037 A, which corresponds to choice B.

Solve for I1 and I2 in the Following Equation: 100I1