Question

prosze rozwiążcie mi układy równań równania: e) 10(y+2)+x -5 =x-5 25(y+2)+3(x-5)= -10 g)x+2y//4 - (x-1/3)=1+y y+3//6 + 2-x//8=3/2

h) 11(3X-2y)+18(2x-3y)=117

27(2x-3y)-2 (3x-2y)=9

Answer 1

e)
10y + 20 + x - 5 = x - 5
25y + 50 + 3x - 15 = -10

 

10y + x - x = -5 - 20 + 5
25y + 3x = -10 - 50 + 15

 

10y = -20 /:2

25y + 3x = -45/:(-5)

 

5y = -10

-5y - 15x = 9

 

-15x = -10 + 9

-15x = -1/:9(-15)

 x = 1/15

 

25y +3x = -45

25y + 3 * 1/15 = -45

25y + 3/15 = -45

25y = -45 - 3/15

25y = -45 i 3/15 /:25

y = -45 i 3/15 : 25/1
y = -678/15 * 1/25

y = -678/375

y = -1 i 101/125

 

 

 

g)

x+2y//4 - x + 1/3 = 1 + y / *4

y+3//6 + 2-x//8 = 3/2 / *24

 

x+2y - 4x + 4/3 = 4 + 4y

4(y+3) + 3(2-x) = 36

 

x+2y - 4x + 4/3 = 4 + 4y

4y + 12 + 6 - 3x = 36

 

x + 2y - 4x - 4y = 4 - 4/3

4y - 3x = 36 - 12 - 6

 

-3x - 2y = 2 i 2/3  / * 2

4y - 3x = 18

 

-6x - 4y = 16/3

4y - 3x = 18

 

-9x = 16/3 + 18

-9x = 5 i 1/3 + 18

-9x = 23 i 1/3  /:(-9)

x = 70/3 * 1/9

x = 70/27

x = 2 i 16/27

 

4y - 3x = 18

4y - 3 * 70/3 = 18

4y - 70 = 18

4y = 18 - 70

4y = - 52 /:4

y = 13

 

 

h)

33x - 22y + 36x - 54y = 117

54x - 81y - 6x + 4y = 9

 

69x - 76y = 117  / *77

48x - 77y = 9  / *(-76)

 

5313x - 5852y = 9009

-3648x + 5852y = -684

 

1665x = 8325  / :1665

x = 5

 

48x - 77y = 9

48 * 5 - 77y = 9

240 - 77y = 9

-77y = 9 - 240

- 77y = -231  / :(-77)

y = 3