. Plane and solid analytic geometry . ;+2/ + l>0. 4. 3x-4:y-2>0. 5. 2x-3y <0. 6. a;2 + ?/20. 8. 3x^-\^ > S. 9. a;2-2/2<l. 10. 3aj2-22/20, (2) ;0. Denote the left-hand sides of (1) and (2) by F^ and F^, re-spectively. By Example 2 of § 6, the points whose coordi-nates satisfy (1) are all thepoints which are on the sameside of the line Li:Fi = 0 asthe origin ; similarly, the pointswhose coordinates satisfy (2)are all the points which are onthe opposite side of the lineL2F2 = 0 from the points whose coordinatessatisfy (1) and (2) are the points common to
. Plane and solid analytic geometry . ;+2/ + l>0. 4. 3x-4:y-2>0. 5. 2x-3y <0. 6. a;2 + ?/20. 8. 3x^-\^ > S. 9. a;2-2/2<l. 10. 3aj2-22/20, (2) ;0. Denote the left-hand sides of (1) and (2) by F^ and F^, re-spectively. By Example 2 of § 6, the points whose coordi-nates satisfy (1) are all thepoints which are on the sameside of the line Li:Fi = 0 asthe origin ; similarly, the pointswhose coordinates satisfy (2)are all the points which are onthe opposite side of the lineL2F2 = 0 from the points whose coordinatessatisfy (1) and (2) are the points common to these two sets, namely, those of region Iof the figure. Lying between the lines Li and L2 there are four regions,I, II, III, IV. It is clear from the foregoing that the pairs ofsimultaneous inequalities representing these regions are:. Fig. 9 li^2>0; II f F, > 0, III F,<0; IV f F, 0. 280 ANALYTIC GEOMETRY Example 2. Find the points satisfying simultaneously the inequalities: ?/2-2a? < 0, x + y -1 <0. The equations obtained by replacing the signs 0, 1. 3. 5. 7. f4x-3 < 0,\Sx-\-2y-6 < 0. l2x-y-\-30. |3a!2 + 42/^-12 >0, \2x-3y-\-12>0. i2x-y-S<0,) x + Sy-5
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