mathcalculus 2 years ago HELP! how to solve system of equations x-2y+z=-1 y+2z=-4 x+y+3z=-5 what do we do when there is a missing variable??? :(

1. woody84

what are you solving for??

2. mathcalculus

x,y, and z

3. mathcalculus

I'm not sure what to do since the x is missing.

4. Directrix

Write the system as: x - 2y +z =-1 0x +y+ 2z=-4 x + y + 3z = -5 In the first and third equations, eliminate the variable x. Then, you will have a system of 2 by 2 equations in the unknowns y and z. Of those two equations, eliminate a variable and solve for the other. If you are allowed to use technology, take a look at the online 3 x 3 linear equation system solver at: http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html @mathcalculus

5. Directrix

Question?

6. mathcalculus

thank you

7. mathcalculus

im trying to solve it step by step

8. Directrix

x - 2y +z =-1 0x +y+ 2z=-4 x + y + 3z = -5 x - 2y +z =-1 x - 2y +z =-1 x + y + 3z = -5 --multiply through by -1 -> -x - y - 3z = 5 ---------------- -3y - 2z = 4

9. mathcalculus

ok

10. mathcalculus

i got a little lost. now i know why

11. mathcalculus

i got that, so what about the second equation?

12. Directrix

@mathcalculus Your Task: Solve this system - Just add them. -3y - 2z = 4 y+ 2z=-4 -----------------

13. mathcalculus

it bothers me that the 0x is there.

14. Directrix

Don't look at it. When I eliminated the "x" in equations #1 and #3, the 0x was not an issue.

15. mathcalculus

i got this: -2y=0

16. mathcalculus

but it can't be. it's undefined.

17. Directrix

Note that here: Solve this system - Just add them. -3y - 2z = 4 y+ 2z=-4 ----------------- I excluded the 0x term. It is just a placeholder of sorts.

18. mathcalculus

0/2?

19. mathcalculus

yeah i know.

20. Directrix

-2y = 0 y= 0/2 y = 0--> You have division by 0 and division into 0 mixed up.

21. mathcalculus

so y is 0?

22. mathcalculus

okay i got that step right.

23. mathcalculus

z=2

24. mathcalculus

x=-6

25. mathcalculus

it's wrong... :(

26. Directrix

27. mathcalculus

z=-2

28. mathcalculus

ok hold on.

29. mathcalculus

i got it right! x=1 y=0 z=-2 ! =]

30. mathcalculus

thanks so much! i really aprreciate it!

31. Directrix

You are welcome.