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me123

  • 5 years ago

Could someone please show me how to solve the system by elimination method? 5x+3y=-7 7x-2y=13

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  1. anonymous
    • 5 years ago
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    Certainly. The elimination method allows you to form a new equation with only one of your variables by adding a multiple of one equation to another. First pick a variable you want to get rid of.

  2. me123
    • 5 years ago
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    Could you show me how this is done step by step?

  3. anonymous
    • 5 years ago
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    Yes, pick a variable you'd like to eliminate (x or y).

  4. me123
    • 5 years ago
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    x

  5. anonymous
    • 5 years ago
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    Ok, so checking the coefficients on x in both equations, we can see that if we multiply the first equation by \(\frac{-7}{5}\) We will have a -7 coefficient on our x term. So rewrite the first equation after multiplying it by \(\frac{-7}{5}\)

  6. anonymous
    • 5 years ago
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    If anything I say doesn't make sense, stop me and let me know.

  7. me123
    • 5 years ago
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    ok

  8. anonymous
    • 5 years ago
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    So what do you get when you multiply the first equation by \(\frac{-7}{5}\).

  9. me123
    • 5 years ago
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    do you make the 55 a fraction then cross multiply

  10. anonymous
    • 5 years ago
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    No, multiply both sides of the whole equation by -7/5

  11. anonymous
    • 5 years ago
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    \[\frac{-7}{5}(5x+3) = \frac{-7}{5}(-7)\] And simplify.

  12. anonymous
    • 5 years ago
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    What do you get?

  13. anonymous
    • 5 years ago
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    While you're working it out I'm gonna grab some coffee.

  14. me123
    • 5 years ago
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    35+3 =-49

  15. anonymous
    • 5 years ago
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    You forgot to (a) change the signs (it was a -7) (b) put each of those over 5 (and simplify the 35) (c) keep your x.

  16. anonymous
    • 5 years ago
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    It should be: \[\frac{-7}{5}(5x + 3y) = \frac{-7}{5}(-7)\] \[\frac{-7}{5}(5x) + \frac{-7}{5}(3y) = \frac{49}{5}\] \[-7x - \frac{21}{5}y = \frac{49}{5}\]

  17. anonymous
    • 5 years ago
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    Right?

  18. me123
    • 5 years ago
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    yes

  19. anonymous
    • 5 years ago
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    Ok, now add this equation to the other one. \(7x\ - 2y = 13\) + \(-7x - (21/5)y = 49/5\) ============== For now don't bother to try to combine the fractions and non-fractions, just eliminate the x.

  20. me123
    • 5 years ago
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    ok

  21. anonymous
    • 5 years ago
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    What do you get for the new equation that only has y's?

  22. me123
    • 5 years ago
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    13/7(7x+2y)=13/7(13)

  23. me123
    • 5 years ago
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    is this step right

  24. anonymous
    • 5 years ago
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    No. Just add the two equations from top to bottom: \(7x \ - 2y \) = 13 + \(-7x - (21/5)y = 49/5\) =============== \(0x - 2y - (21/5)y\) = 13 + 49/5

  25. me123
    • 5 years ago
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    oh ok

  26. anonymous
    • 5 years ago
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    Now multiply that whole equation by 5 to get rid of the fraction

  27. anonymous
    • 5 years ago
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    What do you get?

  28. anonymous
    • 5 years ago
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    The equation on the bottom that only has y's that is.

  29. me123
    • 5 years ago
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    so if i multiply all by 5 I get 10y -10=65+245

  30. anonymous
    • 5 years ago
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    No. 5*(-2y) = -10y 5*(-21/5)y = -21y 5*13 = 65 (this part you did correctly) 5*49/5 = 49 So the equation would be -10y -21y = 65 + 49

  31. anonymous
    • 5 years ago
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    Then you combine your terms.

  32. me123
    • 5 years ago
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    -31y=114

  33. anonymous
    • 5 years ago
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    Right, and now y =?

  34. anonymous
    • 5 years ago
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    Just leave it as a fraction.

  35. me123
    • 5 years ago
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    -31/114

  36. anonymous
    • 5 years ago
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    Yep. Now plug that in for y into either one of your original equations and solve for x.

  37. anonymous
    • 5 years ago
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    Err wait, no. It's -114/31

  38. anonymous
    • 5 years ago
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    You need to practice your distribution rules, and working with equations. I suggest http://www.khanacademy.org/video/solving-equations-with-the-distributive-property?playlist=Algebra%20I%20Worked%20Examples

  39. me123
    • 5 years ago
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    thank you

  40. anonymous
    • 5 years ago
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    Of course! =)

  41. amistre64
    • 5 years ago
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    tag! your it

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