lecture5 - independent consistent . (b) Infinitely many...

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Math 006 (Lecture 5) Systems of linear equations in two variables Example 1. Given that the demand function and supply function are ± p - 2 q = 2 p + q = 5 Find the equilibrium. We solve it by two methods: 1. Method of substitution: 2. Method of elimination: 1
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Definition 1. Given the linear system ± ax + by = h cx + dy = k where a, b, c, d, h and k are constants. A pair of number ( x 0 , y 0 ) is a solution of this system if each equation is satisfied by this pair. Example 2. Solve each of the following systems (a) ± x + y = 4 2 x - y = 2 (b) ± 6 x - 3 y = 9 2 x - y = 3 (c) ± 2 x - y = 4 6 x - 3 y = - 18 2
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Theorem 1. The linear system ± ax + by = h cx + dy = k (1) must have (a) Exactly one solution. In this case, we call the system (1)
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Unformatted text preview: independent consistent . (b) Infinitely many solutions. In this case, we call the system (1) dependent consis-tent . (c) No solution. In this case, we call the system (1) inconsistent . Exercise 1. At $0.6 per bottle, the daily supply for mike is 450 bottles, and the daily demand is 570 bottles. When the prices is raised to $0.75 per bottle, the daily supply increases to 600 bottles, and the daily demand decreases to 495 bottles. Assume that the supply and the demand equation are linear. Find the equilibrium. 3...
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lecture5 - independent consistent . (b) Infinitely many...

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