System of equations with three coordinates. (x,y,z) – Khan Academy Help Center

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Jeffrey Whitney

November 14, 2015 19:16

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I'm currently studying for a math exam for becoming an electrician and am stuck on solving a "system of three linear equations".

Example:
x+y = 6
x+z = 8
y+z = 10.

There seems to be nothing here for that.

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2 comments

Jeremi Ramos

November 15, 2015 00:28
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Huh... you're right... i haven't seen that yet... but I just figured it out based on what I know from systems of equations with 2 variables... I got x = 2, y = 4, and z = 6

I solved the first and last equation for 'y'.... Then i set those two resulting expressions equal to each other and simplified to (-x+z=4)... I used that and the middle equation to solve for 'z'.... Once I got the values of 'z' I just solved the other equations one by one using each new solution for one of the other variables...

Maybe there is some other more efficient way of doing it, I don't know... I'm a math newb just starting out in going beyond the basics... I too would like to see something on this in Khan Academy!
Jeffrey Whitney

November 15, 2015 04:37
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Ok, I have an addition to my earlier statement. There IS an example of 3 equations with 3 variables BUT....

ALL of the examples i have seen list something like this:
(equations are just junk for example)
2x+y+3z = 15
x+6y-3z = 12
x-2y+3z = 10

What this would allow you to do is to adjust the first and third equation to eliminate the 'Y'. My problem is
x+y = 6
x+z = 8
y+z = 10

so the first equation has no 'Z', the second equation as no 'Y', the third equation has no 'X'. How do you handle that? I don't know. HELP!!!!!

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