10y=3y+10+6y

First, we combine the terms 3y and 6y to get 9y. 

We can do this because 3 times a number + 6 times that same number = 9 times that number. To show you this, here's a few examples:

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Let's put some random numbers in. 7 and 4.

(3 x 7) + (6 x 7) = (9 x 7)

21+42 = 63

63 = 63

 

(3 x 4) + (6 x 4) = (9 x 4)

12 + 24 = 36

36 = 36

 

Both of these statements are true. This shows us we can do this.

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Back to the question. Let's combine 3y and 6y to get 9y.

10y=3y+10+6y

10y = 9y+10

Now subtract 9y from both sides. We can also do this...I'm not going to show you some examples but you can try it yourself like I did if you'd like 

10y = 9y + 10

-9y    -9y

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y = 10

 

And there you go!