Question

Zad. 9 str. 100 2 gim. niebieska książka .

Rozwiąż układy ruwnań metodą podstawiania :

a)
<2x - 2y = 7
<4x + 3y = 21

b)
<0.04x + 0,3y = 1,4
<0,1x + 3y = 2,3
c)
<2x + 3y = 13
<3x - 2y = 8
d)
<1/2x - 2y = 8
<2x + 5y = 6
e)
<1/2x - 3/4y = 0
<2/3x + 1 1/4y =9
f)
<3x + 4 y = 1 2/3
<6x +3y = 1 1/4

< to jest taka klamra a np . 1/3 to jedna trzecia

Answer 1

a)

2x-2y=7

4x+3y=21

 

2x=7+2y /:2

4x+3y=21

 

x=3,5+y

4(3,5+y)+3y=21

 

x=3,5+y

14+4y+3y=21

 

x=3,5+y

7y=21-14

 

x=3,5+y

7y=7/:7

 

x=3,5+y

y=1

 

x=3,5+1

y=1

 

x=4,5

y=1

 

b)

0,4x+0,3y=1,4/*10
0,1x+3y=2,3/*10

 

4x+3y=14

x+30y=23

 

4x+3y=14

x=23-30y

 

4(23-30y)+3y=14

x=23-30y

 

92-120y+3y=14

x=23-30y

 

-117y=14-92

x=23-30y

 

-117y= -78/:(-117)

x=23-30y

 

y= 78/117

x=23-30*78/117

 

y=78/117

x=23- 20

 

y=78/117

x=3

 

c)

2x+3y=14
3x-2y=8

 

2x=14-3y/:2

3x-2y=8

 

x=7-1,5y

3(7-1,5y)-2y=8

 

x=7-1,5y

21- 4,5y-2y=8

 

x=7-1,5y

-6,5y=8-21

 

x=7-1,5y

-6,5y=-13/:(-6,5)

 

x=7-1,5y

y= 2

 

x=7-3

y=2

 

x=4

y=2

 

d)

1/2x-2y=8
2x+5y=6

1/2x=8+2y/*2

2x+5y=6

 

x =16+4y

2(16+4y)+5y=6

 

x=16+4y

32+8y+5y=6

 

x=16+4y

13y=6-32

 

x=16+4y

13y= -26/:13

 

x=16+4y

y=-2

 

x=16-8

y=-2

 

x=8

y=-2

 

e)

1/2x-3/4y=0
2/3x+1 i 1/4y=9

 

1/2x=3/4y  /*2

2/3x+1 1/4y=9

 

x=6/4y

2/3*6/4y+1 1/4y=9

 

x=6/4y

1y+1 1/4y=9

 

x=6/4y

2 1/4y=9/*4/9

 

x=6/4y

y=4

 

x=6/4*4

y=4

 

x=6

y=4

 

f)

3x+4y= 1 i 2/3
6x+3y= 1 i 1/4

 

3x=5/3-4y  /:3

6x+3y=1 1/4

 

x=5/9-4/3y

6(5/9-4/3y)+3y=1 1/4

 

x=5/9-4/3y

10/3-8y+3y=1 1/4

 

x=5/9-4/3y

-5y=1 1/4-3 1/3

 

x=5/9-4/3y

-5y=1 3/12-3 4/12

 

x=5/9-4/3y

-5y=-2  1/12/:(-5)

 

x=5/9-4/3y

y=-25/12*(-1/5)

 

x=5/9-4/3y

y=5/12

 

x=5/9-4/3*5/12

y=5/12

 

x=5/9-5/9

y=5/12

 

x=0

y=5/12