We are given 5 independent equations and 6 unknowns currents...

We are given 5 (independent) equations and 6 unknowns. Currents (the I variables) are given in amps and voltage (the V variables) in volts. I = I1 + I2 V1 = 3 I1 V2 = 6 I2 V1 - V2 = 0 V - 17 = V1 Solve (using multiple substitutions) to find I in terms of V and no other variables. I= V+ (within three significant digits) If we are giving one more fact (a 6th equation) V= 2 volts what will be the value of I? I= amps (within three significant digits)

Transcript

00:01 Okay, so given our situation, if we were to pull all the variables to the left side of the equation or move all the i's to the right to one side of the equation, my first equation would be i1 minus i2, minus i3, equals zero since there's nothing on that side.

00:17 And then i would get four times i1.

00:20 We can just rewrite this one equals 16.

00:25 And then my last equation would be four times i1 plus four times i2.

00:30 Equals 24.

00:32 Now in these equations, i'm going to keep my first equation that's about as simplified as i can get i1 minus i2, minus i3 equals 0.

00:43 In my middle equation, i could divide by two to each term to simplify a little more, and i'll get two times i1 plus i3 equals 8.

00:55 And then in my third equation, i could divide each term by 4.

00:59 I could do a number less than that, but i want to simplify as much as possible.

01:05 So it can be a little easier to simplify these.

01:08 So i have three equations.

01:13 How can i combine these in order to get just two equations by itself? so what i could do is i'm going to do equation one minus equation three and see what happens.

01:30 So 1 minus 3.

01:34 The i1s would cancel negative i2 minus i2 would be negative 2 i2 negative i 2 negative a 3 minus 0 is negative i 3 equals 0 minus 6 is negative 6 so now i have an equation with two variables i'm also going to subtract equation 2 minus 2 times equation 3 in order to cancel i 1 since i cancelled i 1 and 1 and 3 and now i'm looking in out equation two.

02:06 So i'm just going to rewrite these two times i1 plus i3 equals 8, and then 2 times equation, negative 2 times equation 3, negative 2 i1 minus 2 i2 equals negative 12.

02:21 When i combine these, the i1s will cancel, 0 plus negative 2 i2, negative 2 i2 plus i3, 8 minus 12 is negative 4...

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