Algebra II Help

Discussion in 'Secondary Education' started by Brendan, Nov 2, 2008.

  1. Brendan

    Brendan Fanatic

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    I am helping my daugther with her math homework and for the following question we keep getting the wrong answers according to the back of the book. Can someone please help? (and explain)

    3x+y+z=4
    2x+2y+3z=3
    x+3y+2z=5
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    I'm getting
    x=1, y=2 and z=-1. Does that check?

    (Yep, I went back and checked it. It works.)

    Let me know if my explanation is too fuzzy.
     
  4. Aliceacc

    Aliceacc Multitudinous

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    WHile you check, here's my math: I label each equation with a row number to clarify:

    3x+y+z=4 R1
    2x+2y+3z=3R2
    x+3y+2z=5R3

    Eliminate the x's
    R1 + (-3R3) : -8y - 5z = -11 R4
    R2 + (-2R3) : -4y - z = -7 R5

    Eliminate the z's:
    R4 + (-5R5): y=2

    Substitute into R5: z=-1

    Substitue both into R3: x=1

    Solution: (1, 2, -1)
     
  5. Brendan

    Brendan Fanatic

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    Alice you're the best! That helps so much.
     
  6. Aliceacc

    Aliceacc Multitudinous

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    No problem.

    Does the work make sense?
     
  7. Brendan

    Brendan Fanatic

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    Complete sense. I just made a simple computation mistake, thanks alot.
     
  8. HMM

    HMM Cohort

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    Just out of curiosity, do you ever write them as augmented matrices?

    3x+y+z=4
    2x+2y+3z=3
    x+3y+2z=5

    | 3 1 1 : 4|
    | 2 2 3 : 3|
    | 1 3 2 : 5|

    because then you could use your calculator (if you have something like a ti81 or better) to solve it for you.
     
  9. Aliceacc

    Aliceacc Multitudinous

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    Yes, I sometimes do them by matrices, but there's NO way I was going to type THAT explanation!!

    I was guessing that this early in the year, they would probably not be up to matrices in Algebra II. I know we cover it much later in the year in Precalc.

    (And I don't own that good a calculator.)
     
  10. Brendan

    Brendan Fanatic

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    ok alice if your up to it i have one more for you. I am too busy grading papers to do it right now. But it is

    3r-2s+4t=-6
    r+s+t=5
    2r-7s-3t=13
     
  11. mmswm

    mmswm Moderator

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    The answer is (8, 3, -6). Do you want the work? I'm way to lazy to type it out....but it works the same way as alice's last post..
     
  12. HMM

    HMM Cohort

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    swap rows 1 and 2

    r+s+t=5
    3r-2s+4t=-6
    2r-7s-3t=13

    -3r1+r2->r2
    -2r1+r3->r3

    r+s+t=5
    0r-5s+t=-21
    0r-9s-5t=3

    -2r2+r3->r3

    r+s+t=5
    0r-5s+t=-21
    0r+s-7t=45

    swap r2 and r3

    r+s+t=5
    0r+s-7t=45
    0r-5s+t=-21

    5r2+r3->r3

    r+s+t=5
    0r+s-7t=45
    0r+0s+-34t=204


    -1/34*r3->r3

    r+s+t=5
    0r+s-7t=45
    0r+0s+t=-6


    from r2 we have s=7t+45=7*(-6)+45=3

    and from r1 we have r=-s-t+5=-3-(-6)+5=8

    so the answer is (r,s,t)=(8,3,-6)
     
  13. mmswm

    mmswm Moderator

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    Thank you HMM...I'm lazy tonight (and I have to admit to getting halfway through it by hand and reaching for a TI-89 to finish it).
     
  14. HMM

    HMM Cohort

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    89's are awesome...I first did it on my 89. I wasn't going to post a solution unless i knew that the values of r, s, and t were integers.
     
  15. mmswm

    mmswm Moderator

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    The 89 is more of a hand-held computer. I love it, even though I don't allow my students to use calculators at all. Come to think of it, I only used a basic scientific calculator for most of my undergrad courses, and only used this one when I got to graduate mathematical stats courses.
     
  16. Brendan

    Brendan Fanatic

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    I got the answer. Finally! But I am confused with your work particulary with the -<r3 type thing.
     
  17. HMM

    HMM Cohort

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  18. Aliceacc

    Aliceacc Multitudinous

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    Sorry Brendan, I went to bed.

    I LOVE matrices. But the computer explanation is brutal! One on one, in tutoring, it's not so bad.

    When we discussed our favorite topics to teach, I completely forgot about this one!
     
  19. senseijoao

    senseijoao Rookie

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    Nov 8, 2008

    Check out the voyager, too. If you need more "computer" in your calculator, it's worth it.
     
  20. Aliceacc

    Aliceacc Multitudinous

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    OK, I'm about to make some enemies :)

    As a high school math teacher, I really don't need a calculator more complicated than a $15 scientific one.

    The only place in my life where I'm doing 3x3 systems of equations, or anything that mathematical, is in a classroom. And my school, fortunately for me, is big on teaching the kids the process. So they can use calculators to help with the arithmetic, but they do the matrices by hand.
     
  21. mmswm

    mmswm Moderator

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    Alice...I feel the same way for teaching...I just get lazy sometimes...and that's exactly what reaching for a calculator is...pure laziness. I don't even allow 4 function calculators into my classroom. The TI-89 is nice because it throws the answers back in symbolic form, so if you have a free variable, it will let you know in terms of X.

    I own the thing for its statistics capabilities. Crunching those kinds of numbers by hand can be horrid, and it's nice to have something that is capable of it that I can throw in my back pocket.
     
  22. Aliceacc

    Aliceacc Multitudinous

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    Our kids aren't allowed calculators in class until they hit the Trig chapter in Geometry, sophomore year.
     
  23. Brendan

    Brendan Fanatic

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    I think it is important though, that the kids no how to use calculators. We allow them to use calculators for everything, and starting in Algebra I we begin training them to use the TI 84.
     

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