Consider the linear grammar
({S, B}, {a, b}, S, {S
aS, S
B, B
bB,
B
}).
A derivation using this grammar might look like this:
Each of {S, aS, aB, abB, abbB, abb} is a sentential form.
Because this grammar is linear, each sentential form has at most one variable. Hence there is never any choice about which variable to expand next.