wz
Θνslo pψνkladu:

1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20;
21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37

 

1)


3[2(3x – 6) -2(4x - 5) + 1] – 3 = 6 [3 – 8(x – 3)]

3 [6x – 12 – 8x + 10 +1] – 3 = 6 [3 – 8x + 24]

18x – 36 – 24x + 30 + 3 – 3 = 18 – 48x + 144

-6x – 6 = - 48x + 162

x = 4

 

 

 

Zk:

L = 3 [2( 12 – 6) – 2(16 – 5) + 1] – 3

L = 3 [ 12 – 22 + 1 ] - 3

L = - 30

P = 6 [ 3 – 8 (4 – 3)]

P = - 30

 

L = P



2)

 


5 {5 [ 5 ( 5x – 4) – 4 ] – 4 } = 5

5 {5 [ 25x – 20 – 4 ] – 4 } = 5

5 {125x – 100 – 20 ] – 4 } = 5

5 {125x – 100 – 20 ] – 4 } = 5

625x – 500 – 100 – 20 = 5

625x = 625

x = 1

 

Zk:

L = 5 {5 [ 5 ( 5 · 1 – 4) – 4 ] – 4 }

L = 5 {5 [ 5 · ( 1 ) – 4 ] – 4 }

L = 5 {5 [ 5 – 4 ] – 4 }

L = 5

P = 5

 

L = P



3)

 


x- (2x – 0,2)2 = 5,8 – (2x + 0,1) (2x – 0,1)

x – (4x2 – 0,8x + 0,04) = 2,8 – 4x2 – 0,01

x – 4x2 + 0,8x – 0,04 = 5,8 – 4x2 – 0,01

x + 0,8x = 5,8 + 0,01 +0,04

1,8x = 5,58

x = 3,25

 

 

Zk:

L = 3,25 – (4 ·(3,25)2 – 0,8 · 3,25 + 0,04)

L = - 36,44

 

P = 5,8 – 4 · 3,252 – 0,01

P = -36,46

 

L = P



4)

 

(x – 1)3 + (x – 2)3 + (x – 3)3 = 3 ·(x – 1)(x – 2)(x – 3)

x3  - 3x2 + 3x – 1 + x3 – 6x2  + 12x – 8 + x3 – 9x2 + 27x – 27 = 3 ·(x – 1)(x – 2)(x – 3)

3x3  - 18x2  + 42x – 36 = 3 ·(x – 1)(x – 2)(x – 3)  |:3

x3 – 6x2 + 14x – 12 = (x – 1)(x – 2)(x – 3)

x3 – 6x2 + 14x – 12 = (x2 – 3x + 2)(x – 3)

x3 – 6x2 + 14x – 12 = x3 – 6x2 +11x – 6

3x = 6

x = 2

 


Zk:

L =(2 – 1)3 + (2 – 2)3 + (2 – 3)3

L = 1 – 1

L = 0

 

P = 3(2 – 1)(2 – 2)(2 – 3)

P = 0

 

L = P



 5)

 

                                                        x

                     x             x       1     2 + 2

x   -     x -   2   -    x -  2    -  2        2       =   1                      1

2                2                      2                         2   (x – (x/2))   2         |·2

 

                                     x

x – x + x – x + x + 2 + 2    =  (x – x)  |·2

            2          2        2                   2

 

x – 2x + x + 2 +  x  = 2x – x       |·2

                            2

4 = 2x – x

x = 4

 

Zk:


                                                      4

                     4             4    1     2  + 2

L =  4   -  4 – 2  -  4  - 2 -  2         2   

        2         2              2                

L = 2 – 1 – 0,5

L = 0,5

 

P = 0,5(4 – 4/2)0,5

P = 0,5

 

L = P



 

6)

 


2x – 5   = 0    |· (x + 3)

x  + 3

2x – 5 = 0

x = 2,5

 

 

Zk:

L = 2 · 2,25 – 5

         2,25 + 3

L = 0

 

P = 0

 

L= P



 

7)

 


(x + 5) (x – 6)    =  0

  36 – x2

(x + 5)(x – 6)    = 0

   - (36 + x2)

 

(x + 5)(x – 6)   =  0

     x2 – 36

 

(x + 5)(x – 6)    = 0        |· (x + 6)

(x – 6)(x + 6)

 

x + 5 = 0

x = -5

 

 

 

 

Zk:

L = (- 5 + 5)(-5 – 6)

          36 - (- 5)2

L = 0

 

P = 0

 

L = P

 

 



8)

 


3y2 + y – 11,2  = y + 2(y + 1)

   y + 3,8

3y2 + y – 11,2  = y + 2y + 2

  y + 3,8

3y2 + y – 11,2  = 3y + 2

  y + 3,8

3y2 + y – 11,2  = (3y + 2)(y + 3,8)

3y2 + y – 11,2  = 3y2 + 11,4y + 2y + 7,6

-18,8 = 12,4y

y = - 1,516

 

Zk:

L  = 3(-1,516)2 + (-1,516) – 11,2

         -1,516 + 3,8

L = - 5,82

          2,28

L  = - 2,55

 

P  = -1,516 + 2(-1,516 + 1)

P = - 2,55

 

L  = P



 

9)

 

x + 2 -  2x – 0,8 + 0,6x  - 1,4x = 0,1(3 – x)

                     15

-0,4x + 2 – 2x – 0,8 + 0,6x  = 0,3 – 0,1x

                            15

-0,3x + 1,7 = 2,6x – 0,8             |·15

                            15

-4,5x + 22,5 = 2,6x – 0,8

26,3 = 7,1x

x = 3,704

 

Zk:

L = 3,704 + 2 -  2 · 3,704 – 0,8 + 0,6 · 3,704 – 1,4 · 3,704

                                            15

L = - 0,0702

 

P = 0,1(3 – 3,704)

P = - 0,0704

 

L = P

 


 

10)

 


11(2x – 1,11)    = -0,128

   x + 13

22x – 12,21      = - 0,128

  x + 13

22x – 12,21 = -0,128(x + 13)

22x – 12,21 = -0,128x – 1,664

22,128x = 10,55

x = 0,477

 

 

Zk:

L = 11(2 · 0,477 – 1,11)

            0,477 + 13

L =  - 1,716 

          13,477

L = - 0,127

 

P = - 0,128

 

L = P



 

 

11)

 


x – 1 – 1,5x     =  20 – 2,5x   +  2

          4                    30

x – 2 =  20 – 2,5x  + 1 – 1,5x

                  30               4

x – 2 = 40 – 5x + 15 – 22,5x      |·60

                         60

60x – 120 = 40 – 27,5x + 15

87,5x = 175

x = 2

 

Zk:

L = 2 – 1 – 1,5 · 2

                   4

L = 2,5

 

P = 20 – 2,5  · 2   +  2

            30

P = 2,5

 

L = P



 

 

12)

 


√(-x) = 2 - √ (2 – x)                |2

-x = 4 – 4(√ (2 – x)) + 2 – x    |2

0 = 16 – 16(2 – x) + 4

0 = 36 – 32 + 16x

16x = -4

x = - 0,25      

 

Zk:

L = √ (-(-0,25))

L = 0,5

P = 2 - √ (2 - (-0,25))

P = 0,5

L  =  P

 

 



13)

 

   x     -    x + 1

x – 1            x      =  x + 1

    x      -    x – 1       x – 1

x + 1           x

 

 x2  -  x2  - 1

   x(x – 1)     =  x + 1

 x2  -  x2  - 1        x - 1

  x(x + 1)

x + 1  -  x + 1  =  0

x – 1      x – 1

0 = 0   =>   x   R{(+,-)1,0}


 

14)

 

(9 – 4x2)(x2 – 6x + 9 ) = 0


9 – 4x2 = 0

9 = 4x2

x2  = 9/4

x = √9/4

x1 = (+,-)3/2

(x2 – 6x + 9 )

(x – 3)2 = 0

(3 – 3)2 = 0

x2 = 3

[(+, - )3/2 ;3]


 

 


Zk:

L1 = (9 – 4 · (3/2)2)((3/2)2 – 6 · (3/2) + 9)

L1  = 0(2,25)

L1 = 0

 

P1 = 0

 

L1 = P1

 

L2 = (9 – 4 · 3)(32 – 6 · 3 + 9)

L2 = -3(0)

L2 = 0

 

P2 = 0

 

L1 = P2



 

15)

 


(4x2 + 25)(50 – x2) = 0

 

4x2  + 25 = 0

4x2 = - 25

x1 = √ (-25/4)

 

50 – x2 = 0

x2 = 50

x = √50

x2 = 2?5

 

 

Zk:

L1 = (4· (√ (-25/4))2 + 25)(50 - (√ (-25/4))2)

L1 = 0(56,25)

L1 =0

P1 = 0

 

L1 = P1

 

L2 =(4 · (2√5)2 + 25)(50 – (2√5)2 )

L2 = 0

P2 = 0

 

L2 = P2



16)

 


7x – 3y = 15    |·2

5x + 6y = 27

19x = 57

    x = 3

 

7 · 3 – 3y = 15

3y = 6

y = 2

 

 

Zk:

L1 = 7 · 3 - 3 · 2

L1= 15

P1 = 15

 

L1 = P1

 

L2 = 5 · 3 + 6 · 2

L2 = 27

P2 = 27

 

L2 = P2



17)

 


3x + 2y = 20    |·2

2x + 3y = 20    |· (-3)

6x + 4y = 40

-6x – 9y = - 60

-5y = -20

   y = 4

 

6x + 4 · 4 = 40

6x = 40 – 16

x = 4

 

 

Zk:

L1 = 3 · 4 + 2 · 4

L1 = 20

 

P1 = 20

 

L1 = P1

 

L2 = 2 · 4 + 3  · 4

L2 = 20

 

P2 = 20

 

L2 = P2



18)

 


3(x – 2) + 2y = x + y

4x + 5(y + x) = 3x – 6

3x – 6 + 2y = x + y

4x + 5y + 5x = 3x – 6

2x + y – 6 = 0             |· (-3)

6x + 5y + 6 = 0

-6x – 3y + 18 = 0

6x + 5y + 6 = 0

2y = -24

y = -12

 

2x – 12 – 6 = 0

2x = 18

x = 9

 

 

Zk:

L1 = 3(9 – 2 ) + 2 · (-12)

L1 = - 3

P1= 9 – 12

P1 = - 3

 

L1 = P1

 

L2 = 4 · 9 + 5(-12 + 9)

L2 = 21

P2 = 3 · 9 - 6

P2 = 21

 

L2 = P2



 

19)

 

x – 5y = 7        |· (-1)

x – 5y = 6

-x + 5y = - 7

x – 5y = 6

0 = -1     => nemα rμšenν


 

20)

 

2x – 3 = 5        => y = 2x - 5

4x – 6y = 10                   3

 

4x – 6  · 2x – 5  =  10

                 3     

4x – 12x + 30  = 10

              3

4x – 4x + 10 = 10

0 = 0    => x   R                     

y = 2t – 5

          3      


 

21)

 


x + y + 2z = -1            |· (-2)   |· (-4)

2x – y + 2z = - 4

4x + y + 4z = -2

x + y + 2z = - 1

- 3y – 2z = - 2             |· (-1)

- 3y – 4z = 2

- 2z = 4

z = - 2

 

-3y – 4(-2) = 2

-3y + 8 = 2

-3y = -6

y = 2

 

x + 2 + 2(-2) = -1

x = 1

 

 

Zk:

L1= 1 + 2 - 4

L1= -1

 

P1= -1

 

L1 = P1

 

L2 = 2 · 1 – 2 – 4

L2 = - 4

 

P2 = - 4

 

L2 = P2

 

L3 = 4 · 1 + 2 + 4(-2)

L3 = -2

 

P3 = - 2

 

L3 = P3



 

 

22)

 

2x + y – z = 0                                     |· (-2)

x + y + 2z = 4              |· (-2)

4x + 3y + 2z = 5

2x + y – z = 0

-2x – 2y – 4z = -8

-y – 5z = -8

-4x – 2y + 2z = 0

4x + 3y + 3z = 5

y + 5z = 5

-y – 5z = -8

y + 5z = 5

0 = - 3     nemα ψešenν


 

23)

 


2x + 3y + z = 15          |·7

7x – y + z = 9              |· (-2)

x + 2y + z = 9                         |· (-2)

 

14x + 21y + 7z = 105

-14x + 2y – 2z = -18

23y + 5z = 87

 

2x + 3y + z = 15

-2x – 4y – 2z = - 18

-y – z = -3

 

23y + 5z = 87

-y – z = -3       |·23

5z = 87

-23z = - 69

- 18z = 18

z = -1

 

-y – (-1) = -3

-y = - 4

y = 4

 

x + 2 · 4 + (-1) = 9

x + 7 = 9

x = 2

 

 

 

Zk:

L1= 2 · 2 + 3 · 4 – 1

L1 = 15

 

P1 = 15

 

L1 = P1

 

L2 = 7 · 2 – 4 – 1

L2 = 9

 

P2 = 9

 

L2 = P2

 

L3 = 2 + 2 · 4 – 1

L3= 9

 

P3 = 9

 

L3 = P3



 

 

24)

 


2x – y – z = 0              |· (-2)

4x + 2y + z = 0

x – y + 3z = 0

-4x – 2y + 2z = 0

4x + 2y + z = 0

3z = 0

z = 0

 

 

2x + y – 0 = 0

y = - 2x

 

x + 2x + 3z = 0

3x + 0 = 0

x = 0

 

y = - 2 · 0

y = 0

 

 

 

 

Zk:

L1 = 2 · 0 – 0 - 0

L1 = 0

 

P1 = 0

 

L1 = P1

 

L2 = 4 · 0 + 2 · 0 + 0

L2 = 0

 

P2 = 0

 

L2 = P2

 

L3 = 0 – 0 + 3 · 0

L3 = 0

 

P3 = 0

 

L3 = P3



 

 

25)

 


2x – y + 0z = 6

0x + y + 4z = 8

x + 0y – z = 1

2x + 4z = 14    =>  x = 14 - 4z

                                         2

                              x = 7 – 2z

 

7 – 2z – z = 1

 

-3z = - 6

z = 2

 

x = 7 – 2 · 2

x = 3

 

y + 4 · 2 = 8

y = 0

 

 

 

Zk:

L1 = 2 · 3 – 0 + 0

L1 = 6

P1 = 6

 

L1 = P1

 

L2 =0 + 4 · 2

L2 = 8

P2 = 8

 

L2 = P2

 

L3 = 3 – 2

L3 = 1

P3 = 1

 

L3 = P3

 



 

26)

 


1    +    3    =  5           a  = 1

x          y                             x

2    -    6    =  6           b  = 1

x          y                             y

a + 3b = 5       |· (-2)

2a – 6b = 6

-2a – 6b = - 10

2a – 6b = 6

-12b = - 4

b = 1

      3

 

2a – 6 · (1/3) = 6

2a – (6/3) = 6

2a = 8

a = 4

 

a  = 1               4 = 1   

        x                    x

b  = 1               1  =  1

       y               3      y

x = 1                y = 3

      4

Zk:

L1 = 1/(1/4)   +   3/3

L1= 5

 

P1=5

 

L1 = P1

 

L2 = 2/(1/4)   - 6/3

L2 = 6

 

P2 = 6

 

L2 = P2

 

 



 

27)

 


    2     -       5       =   1           a =       1  

 x + y         x – y                               x + y

    1      +      4      =    9          b =      1   

  x + y        x – y         5                    x - y       

2a – 5b = 1

a + 4b = 9       |· (-2)

              5  

-13b = - 13

               5

b = 1/5

 

2a – 5 · 1  = 1

             5

2a = 2

a = 1

 

1 =    1            |· (x + y)

       x + y

1 =    1            |·5(x – y)

5    x – y   

 

x + y = 1

x – y = 5     =>  y = x – 5

x + x – 5 = 1

2x = 6

x = 3

y = 3 – 5

y = -2

 

Zk:

L1 =     2      -       5    

        3 - 2        3 - (-2)

L1 = 1

P1 = 1

 

L1 = P1

 

L2 =     1      +       4   

        3 – 2          3 + 2

L2 = 9

        5

P2 = 9

        5

 

L2 =P2



28)

 

2x – 3y + z + 2u = 0

3x + y – 2z – u = 6

4x – 2y – 3z – 4u = - 6

x + 2y + 3z – 2u = - 7

x + 2y + 3z – 2u = - 7             |· (-2)   |· (-3)   |· (-4)

2x – 3y + z + 2u = 0

3x + y – 2z – u = 6

4x – 2y – 3z – 4u = - 6

 


-2x – 4y – 6z + 4u = 14

2x – 3y + z + 2u = 0

-7y – 5z + 6u = 14

 

-3x – 6y – 9z + 6u = 21

3x + y – 2z – u = 6

-5y – 11z + 5u = 27

 

-4x – 8y – 12z + 8u = 28

4x – 2y – 3z – 4u = - 6

-10y – 15z + 4u = 22


 

-7y – 5z + 6u = 14      |·5                    |·10

-5y – 11z + 5u = 27    |· (-7)

-10y – 15z + 4u = 22                          |· (-7)

 


-35y – 25z + 30u = 70

35y + 77z – 35u = - 189

52z – 5u = - 119

-70y – 50z + 60u = 140

70y + 105z – 28u = - 154

55z + 32u = - 14

 


 

52z – 5u = -119          |· (-55)

55z + 32u = - 14         |·52

-2860z + 275u = 6545

2860z + 1664u = - 728

1939u = 5817

u = 3

 


2860z + 275 · 3 = - 728

2860z = - 5720

z = - 2

 

70y + 105 ·(-2) – 28 · 3 = - 154

70y = 140

y = 2

 

x + 2 · 2 + 3(-2) - 2 · 3 = - 7

x = 1


Zk:


L1 = 2 · 1 – 3 ·  2 – 2 + 2 · 3

L1 = 0

 

P1 = 0

 

L1 = P1

 

L2 = 3 · 1 + 2 + 4 - 3

L2 = 6

 

P2 = 6

 

L2 = P2

 

L3 = 4 · 1 - 2 · 2 + 6 – 4 · 3

L3 = - 6

 

P3 = - 6

 

L3 = P3

 

L4 = 1 + 2 · 2 – 6 – 2 · 3

L4 = - 7

 

P4 = - 7

 

L4 = P4



 

29)

 


     1         +         1          =   3

3 – x + 2y       3 + x – 2y      4

       1         -          1          =  1

3 + x – 2y      3 – x + 2y       4

a =         1           b =        1        

        3 – x + 2y         3 + x + 2y

a + b = 3         |·4

            4

b – a = 1          |·4

            4    

4a + 4b = 3

4b – 4a = 1      => a = 4b - 1

                                        4

4[(4b – 1)/4] + 4b = 3

8b = 4

b = 1

      2

 

4· 0,5 – 4a = 1

a = 1

      4

a =         1           b =        1        

        3 – x + 2y         3 + x + 2y

 

1  =         1        

4       3 – x + 2y

1  =         1        

2      3 + x – 2y   

1  ·  (3 – x + 2y)  =  1    |·4

4

1  ·  (3 + x – 2y)  =  1    |·2

2                               

3 – x + 2y = 4

3 + x – 2y = 2

0 = 0  => x   R            t   R

           

            y = t + 1

                    2   



 

30)

 


x + 1   +    y      =    3              a = x + 1

x + y       x – y        2                     x + y

2  ·  x + 1   -  3 ·      y    = 1     b =    y 

       x + y             x – y     2           x – y

a + b = 3         |· (-2)

            2

2a – 3b = 1

                2     

-2a – 2b = - 6

                    2

2a – 3b = 1

                2    

-5b = - 2,5

b = 1

      2   

a + 0,5  = 3

                2

a = 1

 

1 = x + 1         |· (x + y)

      x + y

1  =     y           |·2(x – y)

2      x – y 

(x + y) = x + 1     => y = 1

(x – y) = 2y

 

x – 1 = 2  · 1

x = 3

 

Zk:

L1 = 3 + 1  +        1  

       3 + 1          3 – 1

L1= 3

       2

 

P1 = 3

       2

 

L1 = P1

 

L2 = 2 ·   3 + 1  -  3 ·     1  

               3 + 1            3 – 1

L2 = 1

       2

 

P2 = 1

        2

 

L2 = P2



 

31)

 


x + y +1   =  125

x – y + 1

x + y + 1  =  25

1 – x + y          

x + y + 1 = 3 (x – y + 1)          |·2

                   2

x + y + 1 = 3(1 – x + y)

2x + 2y + 2 = 3x – 3y + 3

x + y + 1 = 3 – 3x + 3y   

-x + 5y – 1 = 0     =>  x = 5y - 1

4x – 2y – 2 = 0  

 

4(5y – 1) – 2y – 2 = 0

20y – 4 2y – 2 = 0

18y – 6 = 0

y = 1

      3

 

x = 5 ·  1  -  1

            3

x = 2

      3

 

 

Zk:

L1 =    2  +  1  +   1

          3       3        

          2  -  1  +  1

          3     3       

L1 =  3

        2

 

P1 = 3

       2

 

L1 = P1

 

L2 =    2  +  1  +   1

          3       3        

          1 – 2  + 1

                3     3

L2 = 3

 

P2 = 3

 

L2 = P2



 

32)

 


1    +    1    +    1   =  9            a = 1

x          y          z                            x   

2    -    3    +    4   = 11           b =  1

x          y          z                             y

4    +    3    -    2   =  9            c = 1

x          y          z                            z

a + b + c = 9               |· (-2)   |· (-4)

2a – 3b + 4c = 11

4a + 3b – 2c = 9 

 

-2a – 2b – 2c = -18

2a – 3b + 4c = 11

-5b + 2c = -7

 

-4a – 4b – 4c = 36

4a + 3b – 2c = 9

-b – 6c = -27

 

-5b + 2c = -7

-b – 6c = - 27              |· (-5)

-5b + 2c = -7

5b + 30c = 135

32c = 128

c = 4

 

-b - 6 · 4 = - 27

-b = - 3

b = 3

 

a + 3 + 4 = 9

a = 9 – 7

a = 2

 

a = 1   

      x

2 = 1

      x

x = 1

      2

b = 1   

      y

 

3 = 1

      y

y = 1

      3

c = 1

      z

4 = 1

      z

z = 1

      4

 

Zk:

L1 = 1    +        1    +    1   

        1              1          1

        2              3          4

L1 = 9

 

P1 =9

 

L1 = P1

 

L2 = 2   -        3     +   4

       1               1          1

       2               3          4

L2= 11

 

P2 = 11

 

L2 = P2

 

L3 = 4   +        3     -   2

       1               1          1

       2               3          4

L3 = 9

 

P3 = 9

 

L3 = P3



 

33)

 


x + y +1   =  125

x – y + 1

x + y + 1  =  25

1 – x + y          

x + y + 1 = 3 (x – y + 1)          |·2

                   2

x + y + 1 = 3(1 – x + y)

2x + 2y + 2 = 3x – 3y + 3

x + y + 1 = 3 – 3x + 3y   

-x + 5y – 1 = 0     =>  x = 5y - 1

4x – 2y – 2 = 0  

 

4(5y – 1) – 2y – 2 = 0

20y – 4 2y – 2 = 0

18y – 6 = 0

y = 1

      3

 

x = 5 ·  1  -  1

            3

x = 2

      3

 

 

Zk:

L1 =    2  +  1  +   1

          3       3        

          2  -  1  +  1

          3     3       

L1 =  3

        2

 

P1 = 3

       2

 

L1 = P1

 

L2 =    2  +  1  +   1

          3       3        

          1 – 2  + 1

                3     3

L2 = 3

 

P2 = 3

 

L2 = P2



 

34)

 

 


x 2 + y2 = 125

x2 – y2 = 25 

2x2  = 150

x2 = 75

x =  √75

 

(√75)2  - y2 = 25

y2 = 75 – 25

y = √50

 

 

 

 

 

Zk:

L1= (√75)2 + (√50)2

L1 = 125

 

P1 = 125

 

L1 = P1

 

L2 = (√75)2 - (√50)2

L2 = 25

 

P2 = 25

 

L2 = P2



 

35)

 


2x  - 3y  = -1

 7      2       70

2x  +  10y = 16

 7         1        7 

- 2x  +  3y  = -1

   7         2       70

2x  +  10y = 16

 7         1        7 

23y  = 161

 2         70

y = 1

      5

 

2x = 16 – 10 · 1

 7      7             5

2x = 3

 7     7

x = 1

 

 

 

Zk:

L1 = 2 · 1  -  3 · 0,2

          7           2

                   6

L1 =  2   -   10

        7         2

L1 = -  1

          70

 

P1 = - 1

         70          

L1 = P1

 

L2 = 2 · 1  + 10 ·  0,2

          7             1

L2 = 2 + 14

       7      7

L2 = 16

         7

 

P2 = 16

        7 

 

L2 = P2

 



 

36)

 


9x – 3y  = 9     |·4

 2      4      4

-3x – 7y = -9 

18x – 3y = 9

-3x – 7y = -9      |·6

18x – 3y = 9

-18x – 42y = -54

- 45y = - 45

y = 1

 

18x – 3 · 1 = 9

18x = 9 + 3 x

x = 2

      3  

 

 

 

Zk:

               2

L1 =   9 · 3  - 3  · 1

            2         4

L1 = 3 – 3

             4

L1 = 9

       4

 

P1 = 9

       4

 

L1 = P1

 

L2 = -3  · 2  - 7 · 1

               3

L2 = -2 – 7

L2 = - 9

 

P2 = - 9

 

L2 = P2



37)

 


   3        +       2      = 3             a =     1   

x + y          x – z      2                      x + y       

   1       -       10    = 7             b =     1  

x + y          y – z     3                       x – z       

   3       +       5     = - 1           c =      1  

x – z           y – z       4                    y – z

3a + 2b = 3

                2

a – 10c = 7

                3

3b + 5c = - 1

                   4     

3a + 2b + 0c = 3

                         2

a + 0b – 10c = 7         |· (-3)

                        3

0a + 3b + 5c = - 1

                           4 

3a + 2b = 3

                 2

-3a + 30c = - 7 

2b + 30c = - 5,5          |·3

3b + 5c = - 1               |· (-2)

                   4 

 

6b + 90c = - 16,5

-6b – 10c = 0,5 

80c = - 16

c = - 1

        5

                       

-6b – 10(-1/5) = 0,5

b = 1

      4

 

 

a – 10c = 7

                3

a = 1

      3

 

                     

1  =      1          |·3(x + y)

3       x + y

1  =      1          |·4(x – z)

4       x – z

-1 =     1          |· (-5(y – z))

 5      y – z  

x + y = 3

x – z = 4

y – z = -5     => z = y + 5

 

x – y – 5 = 4

x = y + 9

y + 9 +y = 3

2y = - 6

y = - 3

 

x + y = 3

x – 3 = 3

x = 6

 

y – z = - 5

-3 – z = - 5

z = 2

 

 

Zk:

L1 =    3     +      2 

        6 – 3      6 – 2

L1 = 3

       2

 

P1 = 3

       2

 

L1 = P1

 

L2 =    1      -       10

        6 – 3       -3 – 2

L2 = 7

       3

 

P2 = 7

       3

 

L2 = P2

 

L3 =     3     +     5 

        6 – 2     -3 - 2

L3 = - 1

          4

 

P3 = - 1

          4

 

L3 = P3