math---help! 1 question

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21. Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions. (3 points)

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  1. ok, im revealing what my initials truly mean: Teen Titans Robing and Starfire luv/heart

    sry for spamming...

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    posted by TTR+S<3
  2. y = x + 1
    2y = 2x + 2

    Now substitute y = x + 1 into the equation 2y = 2x + 2

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    posted by Neil
  3. 3x + 6 = 2(x+3)

    3x+6 = 2x+6
    0=0

    The variable dropped out and we had a true statement.
    So there will be an infinite number of solutions since the equation is actually an identity, that is, the left side is equal to the right side

    If , however, the variable drops out, and you end up with a false statement, there would be NO solution

    e.g. 2x + 3 = 2(x+5)
    2x + 3 = 2x + 10
    3 = 10 --> false, thus no solution

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    posted by Reiny
  4. thank you Neil!!!:)

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    posted by TTR+S<3
  5. N/P

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    posted by Neil
  6. my first two lines should have said:

    2x + 6 = 2(x+3)

    2x+6 = 2x+6

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    posted by Reiny
  7. TTR+S<3 i luv ur username!

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  8. Thank you guys!!!!!

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    posted by TTR+S<#
  9. x=x
    because even though you don't know the value of x you don't need to so either way its true

    hope this helped <3

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    posted by 2019

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