Pset2Answers - EC115 Methods of Economic Analysis Problem...

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EC115 – Methods of Economic Analysis Problem Set 2, Week 4 – Solutions 1. Find the solution (if it exists) to the following linear systems: (a) y = 2x – 3 2y – 3x = 4 (b) x + 1/3y = 10/3 y = -3x + 10 (c) y = 2x – 4 2y – 4x = 12 Solution: (a) 2(2x – 3) – 3x = 4 4x – 6 – 3x = 4 x = 10 => y = 2(10) – 3 = 17. First equation: If y = 0 => x = 3/2, and if x = 0 => y = -3 Second equation: If y = 0 => x = -4/3 and if x = 0 => y = 2. (b) x + 1/3(-3x + 10) = 10/3 => x – x + 10/3 = 10/3 => x = x y = 3/2x + 2 3/2 -4/3 2 -3 17 10 x y Solution y = 2x – 3
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not independent ; they have the same slope and the same y-intercept. Hence, we have an infinite number of solutions. Graphically, one of the curves lies exactly on the top of the other. c) 2(2x – 4) = 4x + 12 => 4x – 8 = 4x + 12 => -8 12. No solution. If we rearrange the second equation, we get: y = 2x + 6. Compare with the first equation: y = 2x – 4. These functions have the same slope but different y- intercept. We say that the equations are inconsistent . They never intersect, so there is no solution. 10/3
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This note was uploaded on 12/31/2011 for the course ECON MR 102 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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Pset2Answers - EC115 Methods of Economic Analysis Problem...

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