HLRGAATPreISM_35799X_07_ch7

# HLRGAATPreISM_35799X_07_ch7 - Chapter 7 Systems of...

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Chapter 7: Systems of Equations and Inequalities; Matrices 7.1: Systems of Equations 1. The two graphs intersect at approximately Therefore about the year 2002, both projections produce the same level of migration. 2. The two graphs intersect at approximately . Therefore , there will be about 3.1 million migrants in 2002. 3. The two graphs intersect at approximately , which is the solution to the system. 4. The graph is increasing until approximately 1998, then decreasing until approximately 2007, and constant thereafter. 5. Then t would represent time in years and y would represent the number of migrants. 6. Both graphs pass the vertical line test, that is, for each x there is only one y . 7. From the graph, the solution is Using substitution, first solve [equation 1] for x , [equation 3]. Substitute in for x, in [equation 2]: Now substitute (2) in for y in [equation 3]: The solution is: 8. From the graph, the solution is Using substitution, first solve [equation 1] for y , [equation 3]. Substitute in for y, in [equation 2]: Now substitute in for x in [equation 3]: The solution is: 9. From the graph, the solution is Using substitution, first solve [equation 2] for x , [equation 3]. Substitute in for x, in [equation 1]: . Now substitute in for y in [equation 3]: The solution is: 10. From the graph, the solution is Using substitution, first solve [equation 2] for x , [equation 3]. Substitute in for x, in [equation 1]: Now substitute in for y in [equation 3]: The solution is: 11. Since in [equation 2], we can use substitution. Substitute in for in [equation 1]: Now substitute (1) in for x [equation 2]: The solution is: 12. Since in [equation 2], we can use substitution. Substitute in for in [equation 1]: Now substitute (1) in for x in [equation 2]: The solution is: 51 1, ] 3 26 . y 5] 3 1 1 2 1 y 3. 5 x 1 1 ] 3 x 2 5 2 1 2 x 5 2 1 x 5 1. 1 ] 3 x 2 y 3 x 1, 1 . y 5 x 1 y 5 1. 5 x 5 5 1 x 5 1. 6 x 2 1 x 2 5 5 1 1 x 2 y 5 x ea ] 1, ] 1 2 bf . x 5 2 a ] 1 2 b 1 x 1. a ] 1 2 b 8 y 4 1 y 1 2 . 5 1 2 y 2 2 2 y 5 ] 4 1 1 2 y 2 1 ] x 2 y 1 x 5 2 y ] x 1 2 y 5 0 ] 1, ] 1 2 . 1 2 , ] 2 . x 5 3 2 1 ] 2 2 1 7 2 1 x 3 1 7 2 1 x 5 1 2 . 1 ] 2 2 6 a 3 2 y 1 7 2 b 1 4 y 5 1 9 y 1 21 1 4 y 5 1 13 y 26 1 y 2 a 3 2 y 1 7 2 b 2 x 2 3 y 5 7 1 2 x 5 3 y 1 7 1 x 5 3 2 y 1 7 2 1 2 , ] 2 . ] 2, 1 . y 5 1 ] 2 2 1 3 1 y 5 1. 1 ] 2 2 x 2. 2 x 4 1 x 1 1 x 1 3 2 1 1 1 x 1 3 2 y 5 x 1 3 ] x 1 y 5 3 1 ] 2, 1 . 2, 2 . x 5 y 1 x 5 2. 1 y 2 1 y 5 4 1 2 y 5 4 1 y 5 2. 1 y 2 x 2 y 5 0 1 x 5 y 2, 2 . 1 2002, 3.1 2 1 2002, 3.1 2 1 2002, 3.1 2 .

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13. Using substitution, first solve [equation 1] for x , [equation 3]. Substitute in for x, in [equation 2]: Now substitute in for y in [equation 3]: The solution is: 14. Using substitution, first solve [equation 2] for x , [equation 3]. Substitute in for x, in [equation 1]: Now substitute in for y in [equation 3]: The solution is: 15. Since in [equation 1], we can use substitution. Substitute in for y, in [equation 2]: Now substitute (6) in for x in [equation 1]: The solution is: 16. Since in [equation 1], we can use substitution. Substitute in for in [equation 2]: Now substitute (1) in for x in [equation 1]: The solution is: 17. Using substitution, first solve [equation 1] for x , [equation 3].
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HLRGAATPreISM_35799X_07_ch7 - Chapter 7 Systems of...

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