Question

Rozwiąż układy równań (najlepiej metodą przeciwnych współczynników):

1.

{2x-y=3

{-4x+6y=2

2.

{4y-2x+10=0

{2x-y+3=0

3.

{2x+y-3=0

{3x-2y+1=0

4.

{2x+2y-1=0

{3x-2y+2=0

5.

{3x-12y+6=0

{x+y-1=0

6.

{2x+5y=2

{2x-2y=4

7.

{x+2y=3

{3x+15y-12=0

Answer 1

1.{2x -y = 3/2

   {-4x +6y = 2

   {4x - 2y = 6

   { -4x+6y = 2

 

             4y=8/4

               y =2

y = 2

2x - 2 = 3

y= 2

2x = 3+ 2

y=2

x = 5/2 = 2,5

 

2.4y-2x+10 = 0

2x- y +3 = 0

 

            3y + 13 = 0

             3y = -13/3

              y = -13/3

2x - 13/3 +3 = 0

2x = 13/3 - 3

2x = 4  1/3 - 3

2x  = 1 1/3 /2

x = 4/3 x 1/2

x = 2/3

 

3.2x + y - 3 = 0 

  3x - 2y + 1 = 0

  2x + y = 3 /x 2

  3x - 2 y = -1

  4x +2y = 6

  3x - 2y = -1

         7x = 5/7

  x = 5/7

2x5/7 + y = 3

y = 3 - 10/7

y = 3 - 1 3/7

y = 1 4/7

 

4. 2x + 2y - 1= 0

  3x - 2y +2 = 0

    2x = 1

    3x = -2

       5x = - 1 /5

        x = - 1/5

2 x (-1/5) + 2y = 1

2y = 1-2/5

2y = 3/5/2

y = 3/10

 

5. 3x - 12y +6 = 0

x+y - 1 = 0

3x - 12y = -6

x +y = 1/ x (-3)

3x - 12y = -6

-3x - 3y = -3

 

           -15y = -9/(-15)

y = 9/15

x +9/15 = 1

x = 1 -9/15

x =6/15

 

6. 2x +5y = 2

    2x - 2y = 4 / x(-1)

2x+5y = 2

-2x - 2y = 4

     3y = 6/3

y = 2

2x + 12 = 2

2x = 2 - 12

2x = -10/2

x = -5

 

7.  x+2y = 3/ (-3)

    3x +15y - 12 =0

-3x - 6y = -9

3x +15y = -12

       9y = -21/9

y = - 21/9

x + 2 x (-21/9) = 3

x = 3 - 14/3

x =  - 1 1/3

 

Mam nadzieję że pomogłam liczę na naj.

 

 

 

 

 

               

Answer 2

1.

{2x-y=3 /*2

{-4x+6y=2

 

4x - 2y = 6

-4x + 6y = 2

________________

4x - 4x - 2y + 6y = 6 + 2

4y = 8 /:4

y = 2

 

2x - 2 = 3

2x = 5 /:2

x = 5/2 = 2,5

 

2.

{4y-2x+10=0

{2x-y+3=0

 

-2x + 4y = -10

2x - y = -3

_______________

2x - 2x + 4y - y = -10 - 3

3y = -13 /:3

y = -13/3

 

4 * -13/3 - 2x  + 10 = 0

-52/3 - 2x = -10 /*3

-52 - 6x = -30

-6x = -30 + 52

-6x = 22 /:(-6)

x = -22/6 = -11/3

 

 

3.

{2x+y-3=0 /*2

{3x-2y+1=0

 

4x + 2y = 6

3x - 2y = -1

_____________

4x + 3x + 2y - 2y = 6 - 1

7x = 5 /:7

x = 5/7

 

2 * 5/7 + y = 3

10/7 + y = 3 /*7

10 + 7y = 21

7y = 21 - 10

7y = 11 /:7

y = 11/7

 

4.

{2x+2y-1=0

{3x-2y+2=0

 

2x + 2y = 1

3x - 2y = -2

_____________

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

5x = -1 /:5

x = -1/5

 

2 * -1/5 + 2y = 1

-2/5 + 2y = 1 /*5

-2 + 10y = 5

10y = 7 /:10

y = 7/10

 

5.

{3x-12y+6=0

{x+y-1=0

 

3x - 12y = -6

x + y = 1 /*(-3)

 

3x - 12y = - 6

-3x - 3y = -3

__________________

3x - 3x - 12y - 3y = -6 - 3

-15y = -9 /:(-15)

y = 9/15 = 3/5

 

x + 3/5 = 1

x = 1 - 3/5

x = 2/5

 

6.

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

{2x-2y=4

 

-2x - 5y = -2

2x - 2y = 4

________________

2x - 2x - 5y - 2y = 4 -2

-7y = 2 /:(-7)

y = -2/7

 

2x - 2 * -2/7 = 4

2x + 4/7 = 4

2x = 3 3/7

2x = 24/7 /*1/2

x = 12/7

 

7.

{x+2y=3 /*(-3)

{3x+15y-12=0

 

-3x - 6y = -9

3x + 15y = 12

______________

3x - 3x - 6y + 15y = 12 - 9

9y = 3 /:9

y = 3/9 = 1/3

 

x + 2 * 1/3 = 3

x + 2/3 = 3

x = 3 - 2/3

x = 2 1/3