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anonymous

  • 5 years ago

3x+y=1/3 2x-3y=8/3 solve for x & y

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  1. anonymous
    • 5 years ago
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    Do you know how to use the substitution method?

  2. anonymous
    • 5 years ago
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    no

  3. anonymous
    • 5 years ago
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    OK use the first equation and get y by itself... This will be the definition for y that we will substitute into the second equation. I'll show you.

  4. anonymous
    • 5 years ago
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    ok

  5. anonymous
    • 5 years ago
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    \[y=-3x +\frac{1}{3}\]

  6. anonymous
    • 5 years ago
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    Substituting... \[2x + (-3)\big(-3x+\frac{1}{3}\big)=\frac{8}{3}\] Do you see where I substituted the right half of equation #1 for the "y" term in equation 2????

  7. anonymous
    • 5 years ago
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    yes got it so far

  8. anonymous
    • 5 years ago
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    OK can you take it from here? Solve Eqn #2 for x. Then take that number and put in for the "x" in equation #1 to get the number value for "y". Post your answer and I'll check.

  9. anonymous
    • 5 years ago
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    y=-2/3, x=1/3 but not sure if there was an easier way to get 1/3

  10. anonymous
    • 5 years ago
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    let me show you.

  11. anonymous
    • 5 years ago
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    OK (that's the answer I got).

  12. anonymous
    • 5 years ago
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    2x+9x+(-1)=8/3 11x+(-1)=8/3 11x=1 8/3 11x=3 2/3 which then is 3 2/3 divided by 11.

  13. anonymous
    • 5 years ago
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    11/3 divided by 11

  14. anonymous
    • 5 years ago
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    =1/3

  15. anonymous
    • 5 years ago
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    Looking....

  16. anonymous
    • 5 years ago
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    Right... There is no reason to use a mixed fraction on the third line. It looks like you went back to an improper fraction when you cleared the 11 from the left anyway. I always recommended that my students left fractions as improper fractions - much easier to divide by multiplying the inverse of that fraction on both sides.

  17. anonymous
    • 5 years ago
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    so should I have made -1 to be -3/3 ?

  18. anonymous
    • 5 years ago
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    Right - I try to keep things as fractions. You'll get pretty good at it and won't need to write the intermediate step. Eg \[11x + (-1)=8/3 \Rightarrow11x=8/3+1\Rightarrow11x=\frac{(8+3)}{3}\] etc.... You'll get good enough to skip steps mentally (careful!)

  19. anonymous
    • 5 years ago
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    \[\frac{1}{11}*\frac{11x}{1}=\frac{11}{3}*\frac{1}{11}\]

  20. anonymous
    • 5 years ago
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    thank you very much! :)

  21. anonymous
    • 5 years ago
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    No problem. Good luck!

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