# math---help! 1 question

pls help me!

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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