Suppose you equation is something like
[tex] at+3 = bt-6 [/tex]
If you subtract [tex] bt [/tex] and 3 from both sides you have
[tex] at-bt = -9 [/tex]
We can rewrite this as
[tex] (a-b)t = -9 [/tex]
And we want this to be true when [tex] t=6 [/tex], so we have
[tex] 6(a-b) = -9 \iff a-b = \dfrac{-9}{6} = \dfrac{-3}{2}[/tex]
So, you can choose any couple a and b such that
[tex] a-b = \dfrac{-3}{2} [/tex]
For example,
[tex] a = \dfrac{-3}{2},\quad b=0[/tex]
or
[tex] a = 2,\quad b = \dfrac{7}{2} [/tex]
and so on
