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Bieber896

  • one year ago

can someone help me on substituting and eliminating systems of equations?! I'm so confused

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  1. jim_thompson5910
    • one year ago
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    Post the full problem please

  2. Bieber896
    • one year ago
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    x=3y-8 5y=19+4x

  3. Bieber896
    • one year ago
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    @jim_thompson5910

  4. jim_thompson5910
    • one year ago
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    since x is fully isolated, you can replace the x in the second equation with 3y-8 so `5y=19+4x` turns into `5y=19+4(3y-8)`

  5. jim_thompson5910
    • one year ago
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    do you see how to solve for y?

  6. Bieber896
    • one year ago
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    5y=19+12y-32??

  7. Bieber896
    • one year ago
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    but there's two ys

  8. jim_thompson5910
    • one year ago
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    get all the y terms to one side so subtract 12y from both sides to get the y terms to the left side

  9. Bieber896
    • one year ago
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    -7y=19+(-32)?

  10. jim_thompson5910
    • one year ago
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    good, then combine like terms on the right side

  11. Bieber896
    • one year ago
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    -7y=-13

  12. jim_thompson5910
    • one year ago
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    what comes next

  13. Bieber896
    • one year ago
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    divide both sides by -7?

  14. jim_thompson5910
    • one year ago
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    correct

  15. jim_thompson5910
    • one year ago
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    \[\Large -7y = -13\] \[\Large \frac{-7y}{-7} = \frac{-13}{-7}\] \[\Large y = \frac{13}{7}\] Notice how the two negatives divide to make a positive result

  16. Bieber896
    • one year ago
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    so y=1.85

  17. jim_thompson5910
    • one year ago
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    I'd leave it as a fraction because the decimal result is only an approximation

  18. Bieber896
    • one year ago
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    oh ok

  19. Bieber896
    • one year ago
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    so then do I plug that in to the next equation?

  20. jim_thompson5910
    • one year ago
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    yes, you'll plug that into `x=3y-8` to find x

  21. Bieber896
    • one year ago
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    so x=-2 3/7

  22. jim_thompson5910
    • one year ago
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    or x = -17/7 so the solution as an ordered pair is \(\LARGE \left( -\frac{17}{7}, \frac{13}{7}\right)\)

  23. Bieber896
    • one year ago
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    ok thanks so much ! can we just do one more?!

  24. anonymous
    • one year ago
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    yes

  25. jim_thompson5910
    • one year ago
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    sure

  26. Bieber896
    • one year ago
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    y=3x+3 y=2x+1

  27. jim_thompson5910
    • one year ago
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    y is equal to 3x+3 AND it's also equal to 2x+1

  28. jim_thompson5910
    • one year ago
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    since y is equal to those two things, we can set the two equal to each other basically we're performing a substitution

  29. jim_thompson5910
    • one year ago
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    y=2x+1 3x+3 = 2x+1 ... replace y with 2x+1 solve for x to get x = ??

  30. Bieber896
    • one year ago
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    so do I have to get rid of one of the variables?

  31. anonymous
    • one year ago
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    isolate your x

  32. jim_thompson5910
    • one year ago
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    move the 2x over you do this by subtracting 2x from both sides

  33. anonymous
    • one year ago
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    x=___

  34. Bieber896
    • one year ago
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    1x+3=+1

  35. jim_thompson5910
    • one year ago
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    now subtract 3 from both sides to move that 3 to the right side

  36. Bieber896
    • one year ago
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    1x=-2

  37. jim_thompson5910
    • one year ago
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    which is the same as x = -2

  38. Bieber896
    • one year ago
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    yup

  39. Bieber896
    • one year ago
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    then plug it in

  40. jim_thompson5910
    • one year ago
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    now plug that into either equation to find y

  41. Bieber896
    • one year ago
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    so the solution is (-2,3)

  42. Bieber896
    • one year ago
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    or -3 lol my bad

  43. jim_thompson5910
    • one year ago
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    yes it's (-2,-3)

  44. Bieber896
    • one year ago
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    thank you both so much for your help @jim_thompson5910 @tekman1298

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