Question

ROZWIĄŻ UKŁAD RÓWNAŃ METODĄ PRZECIWNYCH WSPÓŁCZYNNIKÓW I SPRAWDŹ OTRZYMANE ROZWIĄZANIE. nIE CHCĘ SAMYCH WYNIKÓW!

a) x+y= 9

x-y = 3

b) 3x + 2y= 2

-3x+y=10
c) 3x+ 2y = 5

2x+ 2y = 2

d) x+4y = 11

2x+ 5y = -10

e) 4x + 5y = -4

6x + 7y = -6

f) 2x - 11y = 73

3x- 4y = 47

g) -2x + 5y = -10

7x- 4y = 8

h) 9x + 8y = 1

5x - 6y = 11

BARDZO PROSZĘ O POMOC !!!

Answer 1

a) x+y= 9

    x-y = 3

_____________

x + x + y - y = 9 + 3

2x = 12 /:2

x = 6

 

6 + y = 9

y = 3

Spr: 6 + 3 = 9

      6 - 3 = 3

 

b) 3x + 2y= 2

    -3x+y=10

____________________

3x - 3x + 2y +y = 2 + 10

3y = 12 /3

y = 4

3x + 2*4 = 2

3x + 8 = 2

3x = -6 /:3

x = -2

 

Spr :  3 * (-2) + 2 * 4 = -6 + 8 = 2

    -3 * (-2) + 4 = 6 + 4 = 10

c) 3x+ 2y = 5 / *(-1)

    2x+ 2y = 2

 

-3x - 2y = -5

2x + 2y = 2

______________

2x - 3x - 2y + 2y = -5 + 2

-x = -3

x = 3

 

3 * 3 + 2y = 5

9 + 2y = 5

2y = -4

y = -2

 

Spr  3 * 3 + 2 *(-2) = 9 - 4 = 5

2 * 3 + 2 *(-2) = 6 - 4 = 2

 

d) x+4y = 11 /*(-2)

    2x+ 5y = -10

 

-2x - 8y = -22

2x + 5y = -10

_______________

2x - 2x - 8y + 5y = -22 - 10

-3y = -32 /:(-3)

y = 32/3

y = 10 2/3

 

x + 4 * 32/3 = 11

x + 128/3 = 11 / *3

3x + 128 = 33

3x = 33 - 128

3x = -95 /:3

x = -95/3

x = -31 2/3

 

Spr : -95/3 + 4 * 32/3 = -95/3 + 128/3 = 33/3 = 11

   2 * (-95/3) + 5 * 32/3 = - 190/3 + 160/3 = -30/3 = -10

 

e) 4x + 5y = -4 / *(-3)

    6x + 7y = -6 / *2

 

-12x - 15y = 12

12x + 14y = -12

_____________________

12x - 12x + 14y - 15y = 12 - 12

-y = 0

y = 0

 

4x + 5 * 0 = -4

4x = -4 /:4

x = -1

 

Spr: 4 * (-1) + 5 * 0 = -4 + 0 = -4

6 * (-1) + 7 *0 = -6 + 0 = -6

 

f) 2x - 11y = 73 / * 3

   3x- 4y = 47 /*(-2)

 

6x - 33y = 219

-6x + 8y = -94

________________

6x - 6x - 33y + 8y = 219 - 94

-25y = 125 /:(-25)

y = -5

 

2x - 11 *(-5) = 73

2x + 55 = 73

2x = 73 - 55

2x = 18 / :2

x = 9

 

Spr: 2 * 9 - 11 * (-5) = 18 + 55 = 73

      3 * 9 - 4 * (-5) = 27 + 20 = 47

 

g) -2x + 5y = -10 / *7

    7x- 4y = 8 / *2

 

-14x + 35y = -70

14x - 8y = 16

__________________

14x - 14x + 35y - 8y = -70 + 16

27y = - 54 /:27

y = -2

 

-2x + 5 * (-2) = -10

-2x - 10 = -10

-2x = -10 + 10

-2x = 0 /:(-2)

x = 0

 

Spr: -2 * 0 + 5 * (-2) = 0 - 10 = -10

      7 * 0 - 4 * (-2) = 0 + 8 = 8

 

h) 9x + 8y = 1  /*3

    5x - 6y = 11 / *4

 

27x + 24y = 3

20x - 24y = 44

___________________

27x + 20x + 24y - 24y = 3 + 44

47x = 47 /:47

x = 1

 

9 * 1 + 8y = 1

9 + 8y = 1

8y = 1 - 9

8y = -8 /:8

y = -1

 

Spr: 9 * 1 + 8 * (-1) = 9 - 8 = 1

     5 * 1 - 6 * (-1) = 5 + 6 = 11