Question: The linear system a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 a 3

The linear system

a₁x + b₁y = c₁a₂x + b₂y = c₂a₃x + b₃y = c₃

of three equations in two unknowns represents three lines L₁, L₂, and L₃ in the xy-plane. Figure 3.1.5 shows six possible configurations of these three lines. In each case describe the solution set of the system.

L3 5 L L1 L L2 L3 12 13 L * t

L3 5 L L1 L L2 L3 12 13 L * t (b) L3 4 = 1 (e) 2 (d) FIGURE 3.1.5. Three lines in the plane (Problem 33). L3 (c) L1= L=13 (f) 12 L

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