Question 1203089
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In many other contexts, the asterisk or star symbol * indicates multiplication.
Example: 2*3 = 6


However, this problem has the star operator redefined as:
x*y = 2x-y
This is a user-defined operator.
It is not to be confused with the multiplication symbol.
So be careful not to assume that y*(3*y) turns into 3y^2


Let's replace x with 3
x*y = 2x-y
3*y = 2(3)-y
3*y = 6-y


This means any time we see 3*y, we can replace it with 6-y.


x*y = 2x-y
x*(3*y) = 2x-(3*y)
x*(3*y) = 2x-(6-y)
x*(3*y) = 2x-6+y
x*(3*y) = 2x+y-6


Next we'll replace x with y so we end up with y*(3*y)
x*(3*y) = 2x+y-6
y*(3*y) = 2y+y-6
y*(3*y) = 3y-6



We're told that y*(3*y) = 6
We'll use the previous equation and this given fact to solve for y.
y*(3*y) = 6
3y-6 = 6
3y = 6+6
3y = 12
y = 12/3
y = 4



Answer: y = 4
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