Question

2 zadania w załączniku HELP

Answer 1

 

2(x-y)=10

x+y=5 - > y = 5-x

2(x-(5-x)=10

2(x-5+x)=10

2(2x-5)=10

4x-10=10

4x=20

x=5, y = 0

 

-x+y=3 - > y=3+x

2x+2y=5

2x+2*(3+x)=5

2x+6+2x=5

4x=-1

x= -1/4, y=2 i 3/4

 

 

 3x+4y=6

-2x+y=-4 / *(-4)
3x+4y=6

8x-4y=16

11x=22

x=2, y=0

 

x+2y=-1

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

x+2y=-1

-6x-2y=-4

-5x=-5

x=1, y=-1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

1)    Metoda podstawiania.

     a)    {  2(x-y) = 10    /:2                                            b)    {   -x +y = 3

             {  x + y = 5                                                               {  2x +2y = 5

       {  x - y = 5                                                                                 {  y = 3 +x

       {  x + y = 5                                                                                {  2x + 2(3 +x) = 5

                 {x = 5 + y                                                               {  y = 3 + x 

                 {5 + y + y = 5                                                        { 2x + 6 + 2x = 5

    { x = 5 + y                                                                                { y = 3 +x

    { 2y = 0      /:2                                                                          { 4x = -1     /: 4

            { x = 5 + y                                                               { x = -¼

            { y = 0                                                                     { y = 3 - ¼

     { x = 5                                                                                    {   x = -¼

     { y = 0                                                                                    {  y = 2¾

 

2)     Metoda przeciwnych współczynników.

      a)   { 3x + 4y = 6                                                     b)   { x + 2y = -1

             { -2x + y = -4       /·(-4)                                            { 3x + y = 2         /·(-2)

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

                 +   { 8x -4y = 16                                                        +   {  -6x -2y = -4

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

                        11x = 22    /:11                                                          -5x = -5      /:(-5)

                             x = 2                                                                           x = 1

                 -2· 2 + y = -4                                                               3·1 + y = 2

                    -4 + y = -4                                                                      3 + y = 2

                         y = 0                                                                           y = -1

                 {  x = 2                                                                             {  x = 1  

                 {  y = 0                                                                             {  y = -1