anonymous
  • anonymous
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Mathematics
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anonymous
  • anonymous
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Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
Directrix
  • Directrix
The object is to eliminate one of the three variables and reduce the system of equations to a 2 by 2 system. After that, the next task is to eliminate one of the remaining two variables.
anonymous
  • anonymous
OK

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Directrix
  • Directrix
(1) x + y + z = -5 (2) x - y + 3z = -1 (3) 4x + y + z = -2
Directrix
  • Directrix
In equations 1 and 2, add the two equations. The y variables will add to 0. x + y + z = -5 x - y + 3z = -1 ----------------- 2x + 4z = -6 --->**
Directrix
  • Directrix
In equations 2 and 3, add the two equations. The y variables there will also add to 0. (2) x - y + 3z = -1 (3) 4x + y + z = -2 ----------------------- 5x + 4z = -3---> **
Directrix
  • Directrix
The variable y has been eliminated. Look back at the work and see if you understand how that was done.
anonymous
  • anonymous
OHHH
Directrix
  • Directrix
The 3 by 3 system has been transformed to a 2 by 2 system: 2x + 4z = -6 --->** 5x + 4z = -3---> **
Directrix
  • Directrix
Look at the z variables. They are both +4z. To eliminate the z variables, multiply each member of one of the two equations by (-1).
anonymous
  • anonymous
MAKES SINCE SO FAR
Directrix
  • Directrix
2x + 4z = -6 ---> Mult by -1 -2x -4z = 6 5x + 4z = -3---> 5x + 4z = -3 --------------- 3x = 3 x = 1
Directrix
  • Directrix
X has been found. Now, we have to find y and z.
anonymous
  • anonymous
OHHH
Directrix
  • Directrix
Using one of the 2 variable equations, substitute 1 in for x and solve for y. 2x + 4z = -6 2*1 + 4z = -6 2 + 4z = -6 -2 -2 --------------- 4z = -8 z = -2
Directrix
  • Directrix
So, x = 1 and z = -2 Go to one of the 3 by 3 equations and substitute in for x and z. Then, you can find y.
anonymous
  • anonymous
WOW I THOUGHT IT WAS LESS THEN THISS HAHA
Directrix
  • Directrix
I chose the first one. (1) x + y + z = -5 1 + y -2 = -5 y -1 = -5 y = -5 + 1 y = -4 (1, -4, -2) You should copy this so that you will have an example to use in similar problems.
anonymous
  • anonymous
HEY IM FIXEN TO GO TO BED WE WILL FINISH THIS TOMORROW PLZ
Directrix
  • Directrix
Also, check out this 3 by 3 online solver. http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html
anonymous
  • anonymous
OK I WILL

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