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Rozwiązania

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  2 0

  sonar 25.3.2016 (00:01)

  a)
  4x + 2y = 6 /*7
  9x - 7y = 25 /*2
  
  28x + 14y = 42
  18x - 14y = 50
  --------------------------- dodaję stronami
  28x + 14y + 18x - 14y = 42 + 50
  
  28x + 18x + 14y - 14y = 92
  
  46x= 92
  
  x= 92 : 46
  
  x= 2
  
  
  
  4x + 2y = 6
  
  4*2 + 2y = 6
  
  8 + 2y = 6
  
  2y = 6 - 8
  
  2y = - 2
  
  y = -2 : 2
  
  y = -1
  
  
  spr.
  
  
  9x - 7y = 25
  L= 9x - 7y = 9*2 - 7*(-1) = 18 + 7 = 25
  P= 25
  25=25
  L=P
  
  
  
  b)
  3x - 2 = 5(2x- y) - 6
  4(x +y -2) = 8
  
  3x - 2 = 10x - 5y - 6
  4x + 4y - 8 = 8
  
  3x -10x + 5y = - 6 +2
  4x + 4y = 8 + 8
  
  -7x + 5y = - 4 /*4
  4x + 4y = 16 /*7
  
  - 28x + 20y = - 16
  28x + 28y = 112
  --------------------------------- dodaję stronami
  -28x + 20y +28x + 28y = - 16 + 112
  
  -28x + 28x + 20y + 28y = 96
  
  48y = 96
  
  y = 96 : 48
  
  y = 2
  
  
  
  
  4(x +y -2) = 8
  
  4(x + 2 - 2) = 8
  
  4x = 8
  
  x= 8 : 4
  
  x= 2
  
  
  spr.
  3x - 2 = 5(2x- y) - 6
  L= 3x- 2= 3*2 - 2= 6 - 2= 4
  P= 5(2x- y) - 6 = 5(2*2 - 2) - 6= 5(4-2) - 6 = 5*2 - 6= 10 - 6= 4
  4=4
  L=P
  
  
  
  c)
  5x + 2y = 13 /*(-3)
  7x + 3y = 17 /*2
  
  
  - 15x - 6y = - 39
  14x + 6y = 34
  --------------------
  -15x - 6y + 14x + 6y = - 39 + 34
  
  -15x + 14x - 6y + 6y = - 5
  
  - x= - 5 /*(-1)
  
  x= 5
  
  
  
  5x + 2y = 13
  
  5*5 + 2y = 13
  
  25 + 2y = 13
  
  2y = 13 - 25
  
  2y = - 12
  
  y= - 12 : 2
  
  y = - 6
  
  
  
  spr.
  7x + 3y = 17
  L= 7x + 3y = 7 * 5 + 3*(-6) = 35 - 18 = 17
  P= 17
  17=17
  L=P
  
  
  
  d)
  2(x-y) - 10 = 4
  x= - 3y + (1+ y)
  
  
  2x-2y - 10 = 4
  x= - 3y +1+y
  
  
  2x- 2y = 4 + 10
  x= -2y + 1
  
  
  2(-2y+1) - 2y = 14
  x= - 2y +1
  
  
  -4y + 2- 2y = 14
  x= -2y +1
  
  
  -6y = 14 - 2
  x= - 2y +1
  
  
  -6y = 12
  x= - 2y +1
  
  
  y = 12 : (-6)
  x= - 2y +1
  
  
  y = - 2
  x= -2*(-2) +1
  
  
  y= -2
  x =4 +1
  
  
  y= -2
  x = 5
  
  
  spr.
  x= - 3y + (1+ y)
  L= 5
  P= -3y +(1 + y) = -3*(-2) + (1 -2) = 6 +(-1) = 6-1= 5
  5=5
  L=P

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