LHS CAT4e ISM-09-final

# LHS CAT4e ISM-09-final - Chapter 9 SYSTEMS AND MATRICES...

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848 Chapter 9 SYSTEMS AND MATRICES Section 9.1: Systems of Linear Equations 1. In 2005, the trend “Unadjusted for Weather” shows a higher ozone level than the trend “Adjusted for Weather.” 2. The ozone level was approximately .056 ppm. 3. {(1998, .060), (2000, .059), (2001, .058), (2003, .059), (2005, .056)} 4. The graph is increasing from 1997 to 1998, 2000 to 2002, and 2004 to 2005. The graph is decreasing from 1998 to 2000 and 2002 to 2004. 5. t would represent time in years and y would represent the ozone level in ppm. 6. Answers will vary. One answer is that the graphs pass the vertical line test. 7. 43 1 3 ( 1 ) 5( 2 ) xy += −+ = Solve equation (2) for y . 2 ) 3 ) yx −+ = =+ Replace y with 5 x + in equation (1), and solve for x . ( ) 43 1 343 5 1 3 4 3 15 13 7 15 13 72 8 4 x x xx x −⇒+ += −⇒ + + =− + ⇒ =− Replace x with 4 in equation (3) to obtain 451 . y =− + = Check : () ( ) 3 ( 1 ) 44 3 1 1 3? 16 3 13 13 13 True = −+= −= () 2 ) 415? 415 55 T r u e −− + = = Solution set: ( ) { } 4,1 8. 34 4 ( 1 ) 13 (2) Solve equation (2) for x . 13 (2) 13 (3) Replace x with 13 y + in equation (1), and solve for y . ( ) 34 43 1 34 4 33 9 4 473 94 73 5 5 y y yy y yy ++= ++ =⇒ +=⇒ Replace y with 5 in equation (3) to obtain 51 38 . x =− + = Check : () ( ) ( 1 ) 3 8 45 4? 24 20 4 44 T r u e +−= +− = = 13 (2) 85 1 3 ? 851 3 13 13 True −− = = Solution set: ( ) { } 8, 5 9. x – 5 y = 8 (1) x = 6 y (2) Replace x with 6 y in equation (1), and solve for y : 58658 8 y ⇒−= = Replace y with 8 in equation (2) to obtain x = 6(8) = 48. Check : 58 ( 1 ) 48 5 8 8 ? 48 40 8 88 T r u e = 6( 2 ) 48 6 8 ? 48 48 True = = = Solution set: ( ) { } 48,8 10. 6 x y = 5 (1) y = 11 x (2) Replace y with 11 x for y in equation (1). 65 6 1 1 5 1 x x −=⇒ − =⇒ −=⇒= Replace x with –1 in equation (2) to obtain y = 11(–1) = –11. Check : ()( ) ( 1 ) 61 1 1 5? 15 T r u e −−− = = 11 (2) 11 11 1 ? 11 11 True = −= − Solution set: ( ) { } 1, 11 −− 11. 81 0 2 2 ( 1 ) 36 ( 2 ) Solve equation (2) for y . ( 2 ) ( 3 ) +

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Section 9.1: Systems of Linear Equations 849 Replace y with –3 x + 6 in equation (1), and solve for x . () 81 0 2 2 036 2 2 83 06 2 38 60 22 38 38 1 xy xx x x x −= −− + = +− = = = Replace x with 1 in equation (3) to obtain 3(1) 6 3. y =− + = Check : () () 2 ( 1 ) 81 103 22 ? 2 22 22 True 36 ( 2 ) 31 3 6 ? 336 66 T r u e += = Solution set: ( ) { } 1, 3 12. 45 1 1 ( 1 ) 25 ( 2 ) Solve equation (2) for y . ( 2 ) ( 3 ) yx + Replace y with –2 x + 5 in equation (1), and solve for x . 1 4525 1 1 41 02 5 1 1 14 25 11 14 14 1 x −−+= = −⇒ =⇒= Replace x with 1 in equation (3) to obtain y = –2(1) + 5 = 3. Check : 1 ( 1 ) 41 53 11 ? 1 11 11 True ( 2 ) 21 3 5 ? 235 55 T r u e = Solution set: ( ) { } 13. 71 0 ( 1 ) 31 0 ( 2 ) Solve equation (1) for y . 0 ( 1 ) 0 ( 3 ) =+ Replace y with 7 x + 10 in equation (2), and solve for x . ( ) 0 3 7 1 0 1 0 21 30 10 20 30 10 20 20 1 x x x −= ⇒ + −= ⇒ +−=⇒ +=⇒ ⇒ =− Replace x with –1 in equation (3) to obtain y = 7(–1) + 10 = 3. Check : 0 ( 1 ) 713 1 0? 73 1 0 10 10 True −−= −− =− () ( ) 0 ( 2 ) 33 1 10 ? 911 0 10 10 True −− = = Solution set: ( ) { } 14. 4 x + 5 y = 7 (1) 9 y = 31 + 2 x (2) Solve equation (2) for y . 31 2 99 93 1 2 ( 2 ) (3) Replace y with 31 2 x + in equation (1), and solve for x . 31 155 10 2 9 9 155 10 45 7 45 74 7 94 97 36 155 10 63 46 92 2 x x ++= + + = ⋅++ = Replace x with –2 in equation (3) to obtain y = ( ) 31 31 4 27 2 9 9 23 .
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LHS CAT4e ISM-09-final - Chapter 9 SYSTEMS AND MATRICES...

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