Why is the system considered linear in this case?

[khdani]

hello,
y(t)=[cos(3t)]*x(t)
x1(t) -> y1(t)=[cos(3t)]*x1(t)
x2(t) -> y2(t)=[cos(3t)]*x2(t)
x3(t) = a*x1(t)+b*x2(t)
x3(t) -> y3(t)=[cos(3t)]*x3(t)=[cos(3t)]*(a*x1(t)+b*x2(t))=
=[cos(3t)]*(a*[cos(3t)]*x1(t)+b*[cos(3t)]*x2(t))
y3(t) not equal a*y1(t)+b*y2(t) but the answers in the book said that
the system is linear? why? am i wrong or there's a mistake in the book?

 

[Kruum]

Check out the last two lines again. You've got a mistake there...

 

[khdani]

i found the mistake, thanks