Question

rozwiąż układ równań

a) x/2=y/3

x+2,5= y

b) x/5-y/4=0

x/2-y/16=5,5

c) (x+y)/3+y/5=-2

(2x-y)/3-3x/4=3/2

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

(3x+1)/5-(3y+2)/4=0

Answer 1

a) x/2 = y/3       | * 6

x+2,5= y            | - 2,5

3x = 2y

x = y - 2,5

3 * (y -2,5) = 2y

3y - 7,5 = 2y

y = 7,5

x = 7,5 - 2,5

x = 5

b) x/5 - y/4 = 0                 |*20

x/2 - y/16 = 5,5                | * 16

4x - 5y = 0

8x - y = 88                   |* 5

4x - 5y = 0

40x - 5y = 440

_________

44x = 440

x = 10

8* 10 - y = 88

y = -8

c) (x+y)/3+y/5=-2                   | * 15

(2x-y)/3-3x/4=3/2                   |*12

5x + 5y  + 3y = -30

8x - 4y - 9x = 18

5x + 8y = -30

x - 4y = 18            | * 2

5x + 8y = -30

2x -8y = 36

_________

7x = 6

x = 6/7

6/7 - 4y = 18

4y = -17 1/7

y = - 120/28 = - 30/7

 

d) (2x-1)/5 + (3y-2)/4 = 2              |*20

(3x+1)/5 - (3y+2)/4 = 0               | * 20

8x - 4 + 15y - 10 = 40

12x + 4 - 15y - 10 = 0

8x + 15y = 54

12x - 15y = 6

________

20x = 60

x = 3

8 * 3 + 15y = 54

15y = 54 - 24

15y = 30

y = 2