This paper investigates bipartite-scaled consensus for leader-follower linear multi-agent systems (MASs) under directed fixed or switching cooperative-competitive topologies. The followers are partitioned into two subgroups with cooperative interactions within each subgroup and competitive interactions across subgroups. Prescribed scaling factors are introduced to achieve specified proportional relationships, thereby relaxing the conventional bipartite consensus condition that forces the two subgroups to converge to equal magnitude but opposite sign. This feature is particularly beneficial for complex systems where different subgroups require distinct influence levels from the leader. When full state information is available, a distributed state feedback controller is developed and consensus conditions are derived via algebraic graph theory and Lyapunov stability theory. For scenarios where states are not directly measurable, an observer-based output feedback controller is constructed and the closed-loop stability is rigorously analyzed. Furthermore, both strategies are extended to switching topologies with corresponding sufficient conditions established. Numerical simulations validate the theoretical findings.