Question

uklady rownan metodaprzeciwnych wspolczynnikow
a)
×+3y=10
{
4x-2y=16
b)

2x+3y=-9
{
5x+4y=-5
c)
4x-3y=17
{
5x+2y=4

d)


2x+5y=13
{
7x+4y=5
​

Answer 1

Odpowiedź:

a)

x+3y=10   /*(-4)

4x-2y=16

-4x - 12y = - 40

4x - 2y = 16

------------------------

- 4x - 12y + 4x - 2y = - 40 + 16

-4x + 4x - 12y - 2y = - 24

- 14y = - 24

y = - 24 : (-14)

y = 1 i 10/14

y = 1 i 5/7

x + 3y = 10

x + 3* 1 i 5/7 = 10

x + 3 * 12/7 = 10

x + 36/7 = 10

x= 10 - 36/7

x= 10 - 5 i 1/7

x= 4 i 6/7

spr.

4x-2y=16

L= 4x - 2y = 4 * 4 i 6/7 - 2 * 1 i 5/7 = 4 * 34/7 - 2 * 12/7 = 136/7 - 24/7 = 112/7 = 16

P = 16

16 = 16

L = P

b)

2x+3y=-9   /*(-5)

5x+4y=-5   /*2

-10x - 15y = 45

10x + 8y = - 10

----------------------------

- 10x - 15y + 10x + 8y = 45 - 10

- 10x + 10x - 15y + 8y = 35

- 7y = 35

y = 35 : (-7)

y = - 5

2x+3y=-9

2x + 3(- 5) = - 9

2x - 15 = - 9

2x= - 9 + 15

2x= 6

x= 6 : 2

x= 3

spr.

5x+4y=-5

L= 5x + 4y = 5 * 3 + 4*(-5) = 15 - 20 = - 5

P= - 5

-5 = - 5

L=P

c)

4x-3y=17   /*2

5x+2y=4  /*-3

8x - 6y = 34

15x + 6y = 12

-------------------------------

8x - 6y + 15x + 6y = 34 + 12

8x + 15x - 6y + 6y = 46

23x = 46

x= 46 : 23

x= 2

4x-3y=17  

4*2 - 3y = 17

8 - 3y = 17

- 3y = 17 - 8

- 3y = 9

y = 9 : (-3)

y = - 3

spr.

5x+2y=4

L= 5x + 2y = 5 * 2 + 2* (-3) = 10 - 6 = 4

P= 4

4=4

L=P

d)

2x+5y=13    /*7

7x+4y=5     /*(-2)

14x + 35y = 91

- 14x - 8y = - 10

----------------------------

14x + 35y - 14x - 8y = 91 - 10

14x - 14x + 35y - 8y = 81

27y = 81

y = 81 : 27

y = 3

2x+5y=13

2x + 5 * 3 = 13

2x + 15 = 13

2x= 13 - 15

2x= - 2

x= - 2 : 2

x= - 1

spr.

7x+4y=5

L= 7x + 4y = 7 * (-1) + 4* 3= - 7 + 12 = 5

P= 5

5=5

L=P

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