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September 21st, 2014, 05:58 AM   #1
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Red face Systems of 3 Linear Equations- solutions

i need help with this question, thanx all

question:
Consider the system of linear equations:

x+y+z=6
3x+2y+z=10
mx+2y+z=n

For what values of m and n does the system of equations have:
1) no solutions?
2) a unique solution?
3) infinitely many solutions?
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September 21st, 2014, 08:34 AM   #2
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Equation 3 less equation 2
$$(m-3)x = n-10$$

So $m \ne 3$ has at one solution for $x$ (you need to check that you get unique solutions for $y$ and $z$).

$m = 3, n=10$ implies that any value of $x$ will work. Again this can be verified (and fine tuned) in the system.

$m=3, n \ne 10$ has no solutions.

Last edited by v8archie; September 21st, 2014 at 08:42 AM.
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September 21st, 2014, 08:34 AM   #3
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Quote:
Originally Posted by Sadia View Post
x+y+z=6
3x+2y+z=10
mx+2y+z=n
Math help sites can't conduct classrooms...

Can you solve this system for x, y and z?

x+y+z=6
3x+2y+z=10
5x+2y+z=12

Show us what you can do...
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September 21st, 2014, 08:55 AM   #4
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Quote:
Originally Posted by Denis View Post
Math help sites can't conduct classrooms...

Can you solve this system for x, y and z?

x+y+z=6
3x+2y+z=10
5x+2y+z=12

Show us what you can do...
-Substitution method-
solve x+y+z=6 for z:
Z=6-x-y
substitute into the other two equations:
so, 3x+2y+z=10; 2x+y=4
and, 5x+2y+z=12; 4x+y=6
solve by eliminating y out of the above two equations:
x=1
then by substituting x into 2x+y=4, you get y= 2, then by substituting both x and y into z=6-x-y you get the value of z which is 3.

so: x=1, y=2 and z=3

i know how to do the basics but its hard for a 10th grader to these kind of questions when ur teacher doesnt explain how to do it
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September 21st, 2014, 10:31 AM   #5
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Quote:
Originally Posted by Sadia View Post
i know how to do the basics but its hard for a 10th grader to these kind of questions when ur teacher doesnt explain how to do it
GOOD work!
Please use proper English, like ur = your; that's for YOUR benefit.

Did you read Archie's answer? Are you ok now?
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September 27th, 2014, 03:55 PM   #6
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Quote:
Originally Posted by Denis View Post
GOOD work!
Please use proper English, like ur = your; that's for YOUR benefit.

Did you read Archie's answer? Are you ok now?
Oh I'm sorry I didn't realize this was a grammar forum..... I'll remember that the next time I go on a MATH forum. And no need to get so mad. I didn't realize saying ur instead of YOUR would mean so much. In the future if you happen to get annoyed with someone's questions just ignore it. This is a math forum, I'm pretty sure that means you come to get help, not to get sour and annoyed remarks from people. You don't want to help? Then mind YOUR own business.
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September 27th, 2014, 05:18 PM   #7
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Well, if that's the way you're taking it, so be it.
Good luck.
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