A system of equations.
Dear Mathematical community,
(x^2)yz+3y-z = 31
(x^2)+(y^2)-z = 11
3xy+zy = 24
I've been working with this problem for the last week or so and it seems every way I approach the problem it becomes over complicated. I've tried every last elimination and substitution method I know along with using inverse matrices. So any help, or constructive comments would be much appreciated.
P.S. I know the real integer solutions to this problem, the real issue is I don't know how to algebraically arrive at said solutions.
The substitution method might be easier than the elimination method in this case because you can easily write equation 2 in terms of , whereas making the variables have the same coefficients could be tiresome.
Originally Posted by iammax27
OK, seeing as this was quite difficult, I've had a go of it.
From equation 2 we can see that
Substituting into the other equations:
Working on the second of these equations:
You will now have to substitute this into
and solve for .
(@ Prove it) I also took substitution as my first approach due to the enormity of work I would have to do to simplify using elimination, however, with the substitution I found myself arriving at two distinctive end results. One, I almost got everything in terms of x but found myself with a polynomial expression to the degree of 7 with 2 extra z's. Then the other way I found myself dealing with a giant complex fraction with x and z still present in the equation (same as before, 2 z's). I showed this to my physics professor and he's still a work in progress. Along with my Math professor, whom I sat with for an upmost of 2 hours trying to solve this problem.
So if anyone can actually work through it and show me their work I would love to see, and discuss said work, however, I know most people don't have lots of free time to spend doing arbitrary mathematics.
Still any thoughts or comments are much appreciated.
(Sorry, I wrote this response before I saw that you had worked it out, but thanks I'll take A look at your answer and get back to you)
@ prove it
Thanks for the help, that was fantastic. I think the problem was that I sometimes become too tunnel visioned that I miss to do things like completing the square. Still thanks for the help.