Hi again,

Sorry to probably be so dense, however I'm now (I think) more confused than before with trying to work this out and fully understand it . . .

I have received the following as answers (some from other people elsewere)

First solution:

**11 - 2 √30 = x - y√30 **

=

y = -[(11 - 2√30 - x) ÷ (√30)]

when x = 11

y = -[(11 - 2√30 - 11) ÷ (√30)]

y = -[(-2√30) ÷ (√30)]

y = -2

Incorrect. y = -(-2) = 2 when x = 11

when x = -11

y = -[(11 - 2√30+ 11) ÷ (√30)]

y = -[(-2√30) ÷ (√30)]

y = 2
Also incorrect. What happened to your 11's? They wouldn't cancel out here.
Second solution:

**11 - 2√30 = x - y√30 **

=

(y - 2√30) = x - 11

or

√30 = (x - 11) ÷ (y - 2)
Incorrect. What happened to the sqrt 30 with the y?
Third solution:

**11 - 2√30 = x - y√30 **

=

__11 - 2√30__ = x - y

√30

__11 - 60 __= x - y (multiplied by √30 ÷ √30)

30

-1.6333 = x - y

y - 1.6333 = x

y = x + 1.6333
Incorrect. You'd have to multiply everything by sqrt 30, not just the 2sqrt(30)
Fourth solution:

**11 - 2√30 = x - y√30 **

=

y = (x√30 -11√30 + 2) ÷ 30
There is nothing wrong with the logic here, but does this help you?
Fifth solution:

**11 - 2√30 = x - y√30 **

=

x = 11 and y = 2
Correct. Can you tell by looking at it? You have a number by itself (11) and a number in front of the sqrt(30) (2). X is the number by itself, so it must represent the 11. Y is in front of the sqrt(30), so it must represent 2.
Aaaarrrgghhh

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