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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] the question is solve the 4x4 system of equation using elimination.

[00:00:26] hi, how r you today

Bill P (Tutor)

[00:00:45] very good, thank you.
What are we working on today?

Guest (Customer)

[00:03:00] well the 4 equations are
a+b+c+d=-1, 3a-b+4c-2d=-2, - 2a+8b-9c+3d=25, and 4a+2b- 3c+d=-9, and we have th solve
the 4x4 system of equations
using elimination

Bill P (Tutor)

[00:03:35] ok, let me write them out on the board first

[00:05:42] does that all look correct?

Guest (Customer)

[00:05:52] yes

Bill P (Tutor)

[00:06:08] ok, have you used the elimination method before?

Guest (Customer)

[00:06:22] yes

Bill P (Tutor)

[00:06:56] good. so we need to start by selecting 2 equations, add them, and eliminate a variable

Guest (Customer)

[00:07:13] okay,

Bill P (Tutor)

[00:07:28] so I labeled the equations 1-4

[00:07:46] which 2 do you think we should start with?

Guest (Customer)

[00:08:31] well, if we do 1 and 2, then
we get rid of the b's first off

Bill P (Tutor)

[00:09:04] good, let's start with that.
Can you write it out on the board?

Guest (Customer)

[00:09:21] hahahaha ill try

Bill P (Tutor)

[00:09:27] go for it!

[00:11:39] hold on

[00:11:53] you need to add the variables in each equation

[00:11:57] like vertical addition

Guest (Customer)

[00:12:30] o ya haha sorry,

[00:13:40] k

Bill P (Tutor)

[00:13:52] good so we eliminated the b variable

[00:14:14] next we need to combine 2 more equations,

[00:14:38] but we should use equations where we can eliminate the same b variable again

Guest (Customer)

[00:15:52] so, could we do, 3 and 4, and
multiply #4 by -2

Bill P (Tutor)

[00:16:37] we could, and that would eliminate both c and d,but

[00:17:15] since we started by eliminating b, we should try to stick with eliminating b

[00:17:33] look at equations 2 and 4

[00:17:39] and try to use those

Guest (Customer)

[00:17:55] k

[00:18:32] did you want me to do that on
the board

Bill P (Tutor)

[00:18:38] oh, yes please

[00:20:41] I think you need to multiply #2 by 2 first

[00:20:56] so you get a -2b

Guest (Customer)

[00:24:41] k

Bill P (Tutor)

[00:24:47] good

[00:25:07] we need 1 more equation with the b variable eliminated

[00:25:23] which reduces the problem to a 3x3 system

Guest (Customer)

[00:25:53] okay,

Bill P (Tutor)

[00:26:11] this time we need to use equation 3

Guest (Customer)

[00:26:50] so, would we use 2 and 3?

Bill P (Tutor)

[00:26:55] yes

[00:27:07] write that out for me on the board as well

Guest (Customer)

[00:28:57] , would be multiply number 2
by 8?

Bill P (Tutor)

[00:29:03] yes

Guest (Customer)

[00:33:19] k

Bill P (Tutor)

[00:33:41] good, now those 3 equations form the new 3x3 system we must solve

[00:34:59] so I labeled those equations 5, 6, 7

[00:35:29] we need to eliminate a variable in those equations to simplify it to a 2x2 system

[00:36:25] let's try to elimiate the varaible d

Guest (Customer)

[00:36:39] hmm, okay,

Bill P (Tutor)

[00:36:46] start with equation 5 & 6

[00:37:10] if you multiply eq 5 by -3

[00:37:28] and add to eq 6, the d variable will be eliminated

[00:38:07] want to write it out and tell me what you get?

Guest (Customer)

[00:39:04] i got -2a-10c=-12

Bill P (Tutor)

[00:39:15] good

[00:39:33] now use eq 5 and eq 7 to eliminate d

[00:40:05] you will need to multiply eq 5 by -13 first

Guest (Customer)

[00:40:31] okie dokie

Bill P (Tutor)

[00:40:39] let me know what you get there

Guest (Customer)

[00:42:20] -30a-42c=48

Bill P (Tutor)

[00:42:28] very good!

[00:42:34] its now a 2x2 system

[00:43:34] now eliminate the a and solve for c

[00:44:25] so you'll have to multiply the top eq by -15

Guest (Customer)

[00:45:38] somehow i got a 2.1

Bill P (Tutor)

[00:45:50] hmmm, i got something different

[00:46:42] is that what you got?

Guest (Customer)

[00:48:00] no, when i multiplied -15
times -12, i got 180, not 60

Bill P (Tutor)

[00:48:34] oh, i see

[00:48:46] it should be a 4 not a -12

[00:48:58] sorry I missed that

Guest (Customer)

[00:49:36] but, when we got the
equation, we got -12 up on
top, or whereever we got that

Bill P (Tutor)

[00:50:30] yes, I think that was a mistake

[00:50:36] we should have got -4

Guest (Customer)

[00:51:14] o i see where i messed up, i
said -3 times -3 was 1, not 9,
my mistake

Bill P (Tutor)

[00:51:29] ok, again, sorry I missed that before

[00:51:43] so now what do you get for c?

Guest (Customer)

[00:52:11] 1

Bill P (Tutor)

[00:52:13] good!

[00:52:29] now use c=1 in this equation and solve for a

Guest (Customer)

[00:53:17] -3

Bill P (Tutor)

[00:53:36] excellent! now use c=1 and a=-3 in equation 5

[00:53:45] to solve for d

Guest (Customer)

[00:54:45] so d would equal -4

Bill P (Tutor)

[00:54:52] very good!

[00:55:08] now use a=-3, c=1, d=-4 in eq 1 to find b

Guest (Customer)

[00:56:20] b=5?

Bill P (Tutor)

[00:56:24] You got it!

[00:56:51] if you want to be thorough, you can check that solution in all 4 original equations

[00:57:11] but that is our solution

Guest (Customer)

[00:57:39] THANK YOU SO MUCH!!!!

Bill P (Tutor)

[00:57:46] you''re welcome

[00:58:11] that was a VERY long problem and I hope I didn't miss a short cut that would have made it easier

[00:58:22] but we grinded it out!

[00:58:31] any questions?

Guest (Customer)

[00:59:13] o ya!! and no, no questions.

[00:59:20]

Bill P (Tutor)

[00:59:39] have a great night, and please rate my session, I'd really appreciate it!

[00:59:44]

Guest (Customer)

[01:00:12] no prob, and also have a great
night

Bill P (Tutor)

[01:00:16] thanks, bye!

Guest (Customer)

[01:00:24] bye