A) x+1 - y+2 = 2(x-y)
----3 ----4---------5

x - 3 - y-3 = 2y - x
--4-------3--------------

b) 7+ x-3y = 2x - x+5
---------4------------3

10(x-y)-4(1-x) = y
-----------3------------
to co przed = to przez 3


c) 3(x-y) + 0,25 = 5x - y+19
------4----------------2-----5---

3x-1 - y+9 = -2x
--5------2---------

Liczby pod kreską ułamkową są dodatnie.

1

Odpowiedzi

2009-12-05T01:51:36+01:00
Nie wiem czy prawidłowo odczytane są przeze mnie zadania bo z zapisu nie jest jasne

a) x+1 - y+2 = 2(x-y)
----3 ----4---------5

(x +1):3 - (y+2):4 = 2(x-y):5 /*60
20(x+10) - 15(y+2) = 24(x-y)
20x +200 -15y -30 = 24x -24y
20x -15y -24x +24y = -170
-4x + 9y = 170 (1 równanie)


x - 3 - y-3 = 2y - x
--4-------3--------------

(x-3):4 -(y-3):3 = 2y -x /*12
3(x-3) -4(y-3) = 2y -x
3x -9 -4y +12 = 2y -x
3x -4y -2y +x = -3
4x -6y = -3 (2 równanie)

-4x + 9y = 170
4x -6y = -3

dodajemy stronami
3y = 167
y = 167 :3
y = 55⅔

Obliczam x
4x -6y = -3
4x = -3 + 6*(167/3)
4x = -3 + 334
4x = 331
x = 331 : 4
x = 82¾

x = 82¾
y = 55⅔

b) 7+ x-3y = 2x - x+5
---------4------------3

10(x-y)-4(1-x) = y
-----------3------------
to co przed = to przez 3


7 + (x-3y ):4 = 2x -(x+5): 3 /*12
10(x-y) - 4(1-x):3 =y /*3

84 + 3(x -3y) = 24x - 4(x+5)
30(x-y) -4(1-x) = 3y

84 + 3x -9y = 24x -4x-20
30x -30y - 4 +4x = 3y

3x-9y -20x = -20 -84
34x -30y-3y = 4

-17x -9y = -104 /*2
34x -33y = 4

-34x -18y = -208
34x -33y = 4
dodaję stronami

- 51y = -204
y = (-204) :(-51)
y = 4
obliczam x
34x -33y = 4
34x = 33y +4
34x = 33*4 +4
34x = 132 +4
34x = 136
x = 136 : 34
x = 4

x = 4
y = 4

c) 3(x-y) + 0,25 = 5x - y+19
------4----------------2-----5---

3x-1 - y+9 = -2x
--5------2---------


3(x -y):4 + 0,25 = 5x : 2 -(y +19) :5 /*20
(3x -1) :5 -(y+9) = -2x /*5

15(x-y) +5 = 50x - 4(y +19)
3x -1 - 5 (y -9) = -10x

15x -15y +5 = 50x -4y -76
3x -1 -5y + 45 = -10x

15x -15y - 50x + 4y = -76 -5
3x -5y +10x = -44

-35x -11y = - 81
13x - 5y = - 44

-35x -11y = - 81
-5y = -44 -13x

-35x -11y = - 81
y = (-44 -13x) : (-5)

-35x -11y = - 81
y = (13x +44) :5

-35x - 11*(13x +44) :5 = - 81
y = (13x +44) :5

-35x - 143x :5 - 484 :5 = -81
y = (13x +44) :5

-35x -28,6x = -81 + 96,8
y = (13x +44) :5

- 63,6x = 15,8
y = ( 13/5)x + 44/5

x = (79/5) : (-318/5)
y = ( 13/5)x + 44/5

x = 79/318
y = (13/5)*(79/318) +44/5

x= 79/318
y = 1027/1590 + 44/5

x= 79/318
y = 1027/1590 + 13992/1590

x= 79/318
y = 15019/1590 = 9 i 709/1590