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Unformatted text preview: 52 PROBLEMS FOR CHAPTER 1 3. are parallel with all points in common, (that is, they are the same plane). We give an example for each of these three cases. In Example 1, we skipped the details of solving the systems because solving two simultaneous equations in two unknowns is familiar to all of us. However, for a system of more equations or more unknowns, we better keep track on all the equations. We convert a system to another equivalent system, i.e. a system which has the same solution set, until we get one which gives us a simple form of the solution set. Example 2.. Find the solution of the system of equations 211:1 — 3:132 + 333 = 20 (1) 4:131 + 2332 — 311:3 = 34 (2) SOLUTION. To solve this pair, we first eliminate 3:1 from equation (2) by subtracting 2 times equation (1) from equation (2). The new equation (2) is then 8.932 .... 5583 = *6 (2") Therefore the original system is equivalent to 9:1 — gem. + $932 2 10 (1”) ...
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