solving a hard problem

mattflint50

Junior Member
Joined
Apr 25, 2005
Messages
60
my teacher gave my class these three equations, and told us to solve for X,Y, and Z.

X+y+Z=4
2x-y+2Z=5
7X+y+7Z=22

I cant seem to find an answer. Ive tried to solve it algebretically, and by using crammer's rule, but it just wont come out. Is it even possible? Please help.

Thanx.
 

pka

Elite Member
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Jan 29, 2005
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8,107
 

mattflint50

Junior Member
Joined
Apr 25, 2005
Messages
60
I understand what you just posted, but if im not mistaken, X,Y, and Z were not actually solved, because if you were to plug those numbers into the equations, it wouldn't come out how it was supposed to.
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, mattflint50!

pka's answer do work . . .

The equations are:
. . . . x + y + . z . = . .4
. . . 2x - .y + 2z . = . .5
. . . 7x + y + 7z . = . 22

He said: . x = r, .y = 1, .z = 3 - r
. . . Plug them in!

. . . . r + 1 + . (3 - r) . = . 4
. . . 2r .- 1 + 2(3 - r) . = . 5
. . . 7r + 1 + 7(3 - r) . = .22 . . . . They check out!

The system has an infinite number of solutions.
 

mattflint50

Junior Member
Joined
Apr 25, 2005
Messages
60
ok i see now, thank you
 
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