Treść zadania

Rozwiązania

• 

  0 0

  rzbyszek 10.12.2010 (20:37)

  a)
  \begin{cases} 6x+y=8 \\ -6x+4y=2 \end{cases}
  --------------------------------------------------------------------------------
  5y=10
  
  y=2
  
  6x+2=8
  
  6x=8-2
  
  6x=6x=1
  
  {x=1,y=2}
  
  
  b)
  
  \begin{cases} 2x+3y=4 \\ 3x+5y=7 \end{cases}
  
  \begin{cases} 2x+3y=4 / \cdot (-3) \\ 3x+5y=7 / \cdot 2 \end{cases}
  
  \begin{cases} -6x-9y=-12 \\ 6x+10y=14 \end{cases}
  
  --------------------------------------------------------------------------------
  y=2
  
  -6x-9 \cdot 2=-12
  
  -6x=-12+18
  
  -6x=6
  
  x=-1
  
  {x=-1,y=2}
  
  
  c)
  
  \begin{cases} x+2y=11 \\ 2x-y=7 \end{cases}
  
  \begin{cases} x+2y=11 \\ 2x-y=7 / \cdot 2 \end{cases}
  
  \begin{cases} x+2y=11 \\ 4x-2y=14 \end{cases}
  --------------------------------------------------------------------------------
  5x=25
  
  x=5
  
  5+2y=11
  
  2y=11-5
  
  2y=6
  
  y=3
  
  {x=5,y=3
  
  
  d)
  \begin{cases} 5x+3y=0 \\ 1,5x+y=2 \end{cases}
  
  \begin{cases} 5x+3y=0 \\ 1,5x+y=2 / \cdot (-3) \end{cases}
  
  \begin{cases} 5x+3y=0 \\ -4,5x-3y=-6 \end{cases}
  --------------------------------------------------------------------------------
  -0,5x=-6
  
  x=12
  
  5 \cdot 12+3y=0
  
  3y=-60
  
  y=-20
  
  {x=12,y=-20}

  Dodawanie komentarzy zablokowane - Zgłoś nadużycie

• 

  0 0

  myszka2x2 10.12.2010 (23:29)

  a) 6x+y=8
  + -6x+4y=2
  ------------------
  0 + 5y = 10
  
  5y = 10 |:5
  y = 2
  
  6x+y=8
  6x + 2 = 8
  6x = 8 - 2
  6x = 6|: 6
  x = 1
  
  x = 1, y = 2
  
  b) + 2x+3y=4
  3x+5y=7
  ------------------
  5x + 8y =11
  
  2x + 3y = 4 | : 2
  x + 1,5y =2
  x = 2 - 1.5y
  
  5x + 8y =11
  5 * (2 - 1.5y) + 8 = 11
  10 - 7,5y + 8y = 11
  -7,5y + 8y = 11 - 10
  0,5y = 1 | : 0,5
  y = 2
  
  2x+3y=4
  2x + 3 * 2 = 4
  2x + 6 = 4
  2x =4 - 6
  2x = - 2| :2
  x = -1
  
  x = -1, y = 2
  
  c) x+2y =11
  + 2x-y=7
  ------------
  3x + y = 18
  
  x+2y =11
  x = 11 - 2y
  
  3x + y = 18
  3 * (11 - 2y) + y = 18
  33 -6y + y = 18
  -5y = 18 - 33
  -5y = -15 | : (-5)
  y = 3
  
  x+2y =11
  x + 2 * 3 = 11
  x + 6 = 11
  x = 11 -6
  x = 5
  
  x = 5, y = 3
  
  d) 5x+3y=0
  1,5x+y=2 | * (- 3)
  
  5x + 3y = 0
  + -4,5x - 3y = - 6
  -------------------------
  -0,5x = - 6
  
  -0,5x = - 6 | : (- 0,5)
  x = 12
  
  5x + 3y = 0
  
  5 * 12 + 3y = 0
  60 + 3y = 0
  3y = - 60 | : 3
  y = - 20
  
  x = 12, y = - 20

  Dodawanie komentarzy zablokowane - Zgłoś nadużycie