14.4 答复----第4章:线性等同和不平等体系

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• 选择节答复----第4章:线性等同和不平等体系

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  答复----第4章:线性等同和不平等体系

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  Section 4.2: Types of Systems of Equations
  ::第4.2节:等式系统类型

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  Review
  ::回顾

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  1. consistent, dependent; coincident
     ::一致、有依赖性; 顺数
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  2. inconsistent, independent; parallel
     ::不一致、独立;平行
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  3. consistent, independent; intersecting
     ::一致、独立;交叉
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  4. inconsistent, independent
     ::前后不一致、独立
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  5. consistent, independent
     ::一致、独立
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  6. inconsistent, independent
     ::前后不一致、独立
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  7. consistent, dependent
     ::一致、有受扶养人
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  8. consistent, dependent
     ::一致、有受扶养人
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  9. consistent, independent
     ::一致、独立
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  10. consistent, independent
      ::一致、独立

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  1. a) Answers will vary. Example: 2x + 3y = 5, 2x – 3y = 5    
     b) Answers will vary. Example: 2x + 3y = 5, 4x + 6y = 10  
     c) Answers will vary. Example: 2x + 3y = 5, 2x + 3y = -3  
     d) x = -1, y = 2 or x + 0y = -1, 0x + y = 2    
     e) Answers will vary. Example: x = -1, 2x + 2y = 2  
     f) Answers will vary. Example: 2x + 2y = 2, 2x - 2y = -6
     ::a) 答案会变化。例如:2x+3y=5,2x-3y=2,2x-3y=3,3y=5,2x-3y=5,2x+3y=5,4x+6y=10c)答复会变化。例如:2x+3y=5,2x+3y=5,2x+3d)x=-1,y=2或x+0y=1,0x+y=2e)答复会变化。例如:x=-1,2x+3y=5,4x+6y=10c)答复会变化。例子:2x+2y=2,2x-2y=6。
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  2. No, if the line is the same, it will have infinite solutions (which fits at least one requirement). 
     ::否,如果线线相同,它将有无限的解决办法(至少符合一项要求)。
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  3. No, there cannot be negative people (or other animals, etc.).
     ::不,不可能有负面的人(或其他动物等等)。
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  4. Sonia: 2a + 3b = 4
     Muhammed: 4a + 6b = 8
     Consistent and dependent
     ::索尼娅:2a+3b=4 Muhammed:4a+6b=8
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  5. Peter: D = 5t + 20
     Nadia: D = 6t
     Consistent and independent
     ::彼得:D = 5t + 20 Nadia: D = 6 一致和独立

   

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  Section 4.3: Solving Systems of Equations by Graphing
  ::第4.3节:通过图表绘制的平方溶解系统

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  Review
  ::回顾

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  1. D, Solution: (-2, 2)
     ::D,解决方案-2,2)
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  2. C, Solution: (3, 0)
     ::C,解决方案3,0)
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  3. A, Solution: (0, 1)
     ::A,解决办法0,1)
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  4. B, Solution: (1, 0)
     ::B,解决方案1,0)
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  5. Solution: (5, -1)
     
     ::解决办法: (5, -1)
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  6. Solution: (3, 2)
     
     ::解决办法3,2)
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  7. Solution: (-1, 3)
     
     ::解决办法-1,3)
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  8. Solution: (4, 0)
     
     ::解决办法: (4,0)
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  9. Solution: (-2, -5)
     
     ::解决办法-2, 5)
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  10. Solution: (-3, 2.5)
      
      ::解决办法-3,2.5)

   

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  1. a) Bargain: $6.50 for 1 hour
         Frugal: $7.25 for 1 hour
         Bargain: $20 for 10 hours
         Frugal: $18.50 for 10 hours
     b)  $\begin{align*}y = 1.5x + 5\end{align*}$  for B
          $\begin{align*}y = 1.25x + 6\end{align*}$  for F
     c) Cost is the same at (4, 11). 4 hours for $11
     d) Bargain Bikes. It will cost $9.50 instead of $9.75.
     :a) 讨价还价:6.50美元,1小时;7.25美元,1小时;20美元,10小时;18.50美元,10小时(b),y=1.5x+5美元,B=1.25x+6美元,F(c)费用不变(4,11小时,4小时,11美元)。
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  2. $\begin{align*}t = 20 \end{align*}$  seconds
     $\begin{align*}D = 120 \end{align*}$  feet
     ::t=20秒 D=120英尺
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  3. $\begin{align*}y = 6.6 \end{align*}$  years
     ::y=6.6岁
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  4.   $\begin{align*}m = 5\frac{1}{3}\end{align*}$    
     ::m=513米=513米

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  Section 4.4: Solving Systems of Equations by Substitution
  ::第4.4节:以替代方式解决等式的系统

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  Review
  ::回顾

  1. (-10, 3)
  2. (0, 6)
  3. (2, -5)
  4. (8, -1)
  5. (4, 7)
  6. (13, -2)
  7. (9, 0)
  8. (-11, 9)
  9. (-3, -6)
  10. (7, 5)
  11. ( $\begin{align*}\frac{1}{2}, 1\frac{1}{3}\end{align*}$ )
  12. (1, 4)
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  13. No solution
      ::无解决方案
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  14. Infinite solutions
      ::无限解决方案

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  1. 
      
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  2. 3 shorts and 4 T-shirts
     ::3短裤和4件T恤衫
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  3. 523 students
     ::523名学生
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  4. A ny number of texts will solve the equation (all solutions, because the equations are dependent).
     ::任何数个文本将解答方程式(所有解决方案,因为方程式取决于方程式)。
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  5.   $\begin{align*}A = 90.\overline{90}\end{align*}$ ,  $\begin{align*}B = 409.\overline{09}\end{align*}$  
     ::A=90,90,B=409,09
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  6. 10 pounds of each type of coffee
     ::每种咖啡10磅

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  Section 4.5: Solving Systems of Equations by Addition
  ::第4.5节:通过加法解决等式的解决系统

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  Review
  ::回顾

  1. (2, -7)
  2. (3, -5)
  3. (10, -11)
  4. (-6, 1)
  5. (9, 4)
  6. (-8, 2)
  7. (6, -2)
  8. (-5, 5)
  9. (4, -9)
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  10. No solution
      ::无解决方案
  11. (0, 0)
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  12. Infinite solutions
      ::无限解决方案

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  1. 3 & 7
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  2. $\begin{align*}x = $0.25\end{align*}$  apples, $\begin{align*}y = $0.30\end{align*}$  oranges 
     ::x=0.25苹果,y=0.30橙子
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  3. 10 movie rentals
     ::10部电影出租
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  4. $\begin{align*}w = 24\end{align*}$  mph 
     ::W=24 英里
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  5. w = $12 per warranty, h = $8.20
     ::w = 每保证金12美元,h = 8.20美元

   

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  Section 4.6:    Solving Systems of Equations by Multiplication and Addition
  ::第4.6节:通过乘数和加法解决等同的解决系统

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  Review
  ::回顾

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  1. x = 6, y = -3 or (6, -3)
     ::x = 6, y = -3 或 (6, 3)
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  2. x = -1, y = 4 or (-1, 4)
     ::x = - 1,y = 4 或 (-1, 4)
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  3. x = -11, y = 5 or (-11, 5)
     ::x = -11,y = 5 或 (-11, 5)
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  4. x = 7, y = 2.5 or (7, 2.5)
     ::x = 7,y = 2.5 或 (7, 2.5)
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  5. x = 2, y = -10 or (2, -10)
     ::x = 2,y = -10 或 2,-10
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  6. x = 48, y = 36 or (48, 36)
     ::x=48,y=36或(48,36)
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  7. x = 8, y = -9 or (8, -9)
     ::x = 8,y = -9 或 (8,-9)
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  8. x = -6, y = -5 or (-6, -5)
     ::x = -6, y = -5 或 (6, 5)
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  9. x =  $\begin{align*}\text{-}\frac{21}{5}\end{align*}$ , y = 0 or  $\begin{align*}(\text{-}\frac{21}{5}, 0)\end{align*}$  or $\begin{align*}(\text{-}4.2, 0)\end{align*}$  
     ::x = - 215 y = 0 或 (-215,0) 或 (-4.2,0)
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  10. x = 12, y = -13 or (12, -13)
      ::x = 12,y = -13 或 (12,-13)
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  11. x = 1, y = 4 or (1, 4)
      ::x=1,y=4或(1,4)
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  12. x = 3, y = 3.5 or (3, 3.5)
      ::x = 3,y = 3.5 或 (3,3.5)
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  13. Same line, infinite solutions
      ::同一直线, 无限的解决方案
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  14. x = -2, y = -11 or (-2, -11)
      ::x = -2,y = -11 或 (-2,-11)
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  15. $\begin{align*}x = \text{-}\frac{12}{64} = \text{-}\frac{3}{16}\end{align*}$ , $\begin{align*}y = \frac{1}{10}\end{align*}$  or $\begin{align*}(\text{-}\frac{3}{16}, \frac{1}{10})\end{align*}$  
      ::x=1264=316,y=110或(-316,110)

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  1. A = 4.875 mL, B = 8.125 mL
     ::A=4.875毫升,B=8.125毫升
  2. $6.75
  3. $6.20
  4. $12 
  5. $5.75

   

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  Section 4.7: Determining the Best Method to Use When Solving a System of Equations
  ::第4.7节:确定在解决公平制度时采用的最佳方法

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  Review
  ::回顾

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  1. x = 3, y = 8 or (3, 8)
     ::x = 3, y = 8 或 (3, 8)
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  2. x = -5, y = -1 or (-5, -1)
     ::x = 5, y = -1 或 (5, 1)
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  3. x = -2, y = 9 or (-2, 9)
     ::x = - 2,y = 9 或 (-2, 9)
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  4. $\begin{align*}x = \text{-}\frac{1}{2}, y = \text{-}\frac{1}{2}\end{align*}$  or  $\begin{align*}(\text{-}\frac{1}{2}, \text{-}\frac{1}{2})\end{align*}$  
     ::x=12,y=12 或 (12, 12)
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  5. x = 4, y = 6 or (4, 6)
     ::x = 4,y = 6 或 (4,6)
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  6. x = 3,  $\begin{align*}y = \text{-}\frac{3}{5}\end{align*}$  or  $\begin{align*}(3, \text{-}\frac{3}{5})\end{align*}$  
     ::x = 3, y=-35 或 (3, 35)
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  7. x = 2, y = 11 or (2, 11)
     ::x = 2,y = 11 或 2, 11)
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  8. x = -8,  $\begin{align*}y = \frac{2}{3}\end{align*}$  or  $\begin{align*}(\text{-}8, \frac{2}{3})\end{align*}$  
     ::x = - 8, y= 23 或 (-8, 23)
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  9. Infinite solutions, same line 
     ::无穷无尽的解决办法,同行同行
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  10. x = 9, y = -2. (9, -2)
      ::x=9,y =-2(9,-2)
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  11. x = 0.286, y = -1 or (0.286, -1)
      ::x=0.286,y=-1或(0.286,-1)
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  12. No solutions; lines are parallel
      ::否解决方案; 线条是平行的

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  1. x = 26, y = 9; numbers are 26 & 9
     ::x = 26,y = 9;数字为 26 & 9
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  2. cars = 12, vans = 15
     ::12辆面包车=15辆
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  3. cappuccinos = 5, lattes = 4
     ::卡布奇诺=5,拿铁=4
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  4. w = 46.875 mph
     ::w = 46.875 毫时
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  5. $\begin{align*}\frac{1}{2}\end{align*}$  pint whole and  $\begin{align*}\frac{1}{2}\end{align*}$  pint skim
     ::12品脱整和12品脱滑
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  6. monthly pass = $100, ride when paying per ride = $2.25
     ::每月通行证 = 100美元,每次出车时乘车 = 2.25美元

   

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  Section 4.8: Solving Systems of Linear Inequalities
  ::第4.8节:线性不平等的解决系统

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  Review
  ::回顾

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  1. a) Yes.  b) No.  c) No.  d) Yes.
     :a) 是(b) 否(c) 否(d) 是。
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  2. a) Yes.  b) No.  c) No.  d) No.
     :a) 是(b) 否(c) 否(d) 否(c)
  3. 
     
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  1. 
     
  2. 
     
  3. 
     

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  Section 4.9: Solving Linear Systems of Three Variables
  ::第4.9节:三个变量的溶解线性系统

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  Review
  ::回顾

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  1. $\begin{align*}x=\text{-}4,y=1,z=6\end{align*}$  
     ::x=4,y=1,z=6 x=4,y=1,z=6
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  2. $\begin{align*}x = 5, y = 9, z = \text{-}2\end{align*}$  
     ::x=5,y=9,z=2x5,y=9,z=2
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  3. $\begin{align*}x = 2, y = 1, z = 2\end{align*}$  
     ::x=2,y=1,z=2
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  4. $\begin{align*}y = \text{-}\frac{3}{2}x - 4, z = 0\end{align*}$  
     ::y=-32x-4,z=0
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  5. $\begin{align*}x = \text{-}7, y = 5, z = 4\end{align*}$  
     ::x=-7,y=5,z=4
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  6. $\begin{align*}x = 1, z = \text{-}y-4\end{align*}$  
     ::x=1,z=-y-4x=1,z=-y-4
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  7. no solutions exist
     ::不存在任何解决方案
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  8. $\begin{align*}y = \text{-}x - 1, z = \text{-}x - 2\end{align*}$  
     ::y=-x-1,z=-x-2
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  9. $\begin{align*}x = 4, y = \text{-}2, z = 1\end{align*}$  
     ::x=4,y=2,z=1x4,y=2,z=1
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  10. $\begin{align*}y = 3 - x, z = 0\end{align*}$  
      ::y=3 - x,z=0

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  1. Swim: 1.25 hours, or 1 hour and 15 minutes
     Bike: 2 hours
     Run: 1.5 hours, or 1 hour and 30 minutes
     ::游泳:1.25小时,或1小时15分钟,Bike:2小时运行:1.5小时,或1小时30分钟
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  2. Approximately: 
     43.6 bushels of wheat
     207.3 bushels of corn
     42.1 bushels of soybeans
     ::大约:小麦43.6桶