Question

One more:Find the solution to the system of equations represented by the matrix shown below. Use the matrix tool.

Answer 1

you just gotta row reduce it

Answer 2

im not quite sure what the matrix tool does tho

Answer 3

still trying to solve it.

Answer 4

Use the process of Gaussian elimination ( http://en.wikipedia.org/wiki/Gaussian_elimination). It is tedious, annoying, and rather prone to mistakes... But that's the quickest method. Using substitution will not get you anywhere unless you're able to find an ingenious substitution.

Answer 5

whats slowing you down? :)

Answer 6

I presume Andres is new to this?

Answer 7

says hes been doing this for at least 30 minutes; plenty o time

Answer 8

It's very easy to make a bunch of correct moves and then mess up a simple operation.

Answer 9

its prolly the matrix tool, just cant beat pencil and paper

Answer 10

Pencil and paper are powerful, I agree.

Answer 11

sorry, i was working on another problem. but i was planning on doing it like this one.
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try to eliminate x 1st 6 x equation (1) + equation (3) gives 10y + 10y = 170 (4) then equation (2) + equation(3) gives 5y + 12z = 127 (5) then its (4) - 2 x (5) 10y + 10z = 170 - 10y + 24z = 254 -14z = -84 z = 6 sub into (4) to find y 10y + 10(6) = 170 10y = 110 y = 11 sub y = 11 and z = 6 into equation 1 to find x x + 11 + 6 = 22 x = 5 the solution x = 5, y = 11 z = 6

Answer 12

Here's a cute way to save time: Since we have four choices, we can simply use logic to eliminate them.

Obviously A is not the right answer: \(y=30\) implies that, in the second equation, we have \(5x+120+7z=81\). Noticing that both \(x\) and \(z\) are also positive in answer A, we can safetly conclude A is not the right answer.

Now just randomly pick between B, C, and D. I picked B first, because it looked cool. You can check it via the first equation: \(1\cdot 5+2\cdot 7-2\cdot 4=5+14-8=11\). This tells us that B is possibly true. Now check it for equation 2 and 3: \(5 \cdot 5+4\cdot 7+7 \cdot 4=25+28+28=81\). So, now, if it's true for 3, we are done. Check: \(-4 \cdot 5 + 1 \cdot 7-6\cdot 4=-20+7-24=-37\). Thus, B.

I would do a more rigorous Gaussian elimination, had it been a non-multi-choice question. However, I feel that employing common sense here is a good idea (i.e. instead of doing a Gaussian elimination, simply try the choices).

Answer 13

I will be honest with you and admit that solving linear systems (or quadratic systems for that matter) is nothing more than a basic conceptual understanding of substitution and being able to perform arithmetical operations well. It is rare that any "intelligence" is involved, so do not feel bad if you screw up one of these problems. It happens to everyone (when I was studying this, I once spent three sheets of paper on one system).