Question

1.Uporzadkuj i razwiaz układy równań

a)

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

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

b)

{-x+y+7=2x+3y+9

{2x+y+10=-4x+3y+30

c)

{3x-4y+6=x-3y+7

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

d)

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

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

Answer 1

a)

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

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

 

x+y=6

2x+4y=-2

 

x=6-y

2(6-y)+4y=-2

12-2y+4y=-2

2y=-14

y=-7

 

x=6-(-7)

x=13

 

b)

{-x+y+7=2x+3y+9

{2x+y+10=-4x+3y+30

 

-3x-2y=2

6x-2y=20/:(-2)

 

y=-10+3x

-3x-2(-10+3x)=2

-3x+20-6x=2

-9x=-18

x=2

 

y=-10+3*2

y=-10+6

y=-4

 

c)

{3x-4y+6=x-3y+7

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

 

2x-y=1

-3x+y=-3

 

y=-3+3x

2x-(-3+3x)=1

2x+3-3x=1

-x=-2

x=2

 

y=-3+3*2

y=-3+6

y=3

 

d)

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

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

 

-3x-3y=-9/:(-3)

-5x+2y=3

 

x=3-y

-5(3-y)+2y=3

-15+5y+2y=3

7y=-12

y=-1⁵/₇

 

x=3-(-1⁵/₇)

x=4⁵/₇

 

 

Answer 2

a) {x+4y+2=2+3y+6

    {3-x+2y=1-3x-2y

     

   

     {x+4y-3y= -2+2+6

     {-x+3x +2y+2y = -3+1

     {x+y=6

     {2x+4y=-2

      x=6-y

      2(6-y)+4y=-2

      12-2y+4y=-2

      2y=-12-2

      2y=-14/2

        y= -7

 

       x= 6-(-7)

       x= 13

 

b)  {-x+y+7=2x+3y+9

     {2x+y+10=-4x+3y+30

 

     {-x-2x+y-3y=9-7

     {2x+4x+y-3y=30-10

     {-3x-2y=2

     {6x-2y=20

 

      -6x-2y=20

      -2y=20-6x /-2  

         y=-10+3x

 

        -3x-2(-10+3x)=2

        -3x+20-6x=2

        -9x=-20+2

        -9x=-18/-9

           x=2

 

           y=-10+3*2

           y=-10+6

           y= -4

      

c)      {3x-4y+6=x-3y+7

         {4-x-y+2x-2y+1

 

         {3x-x-4y+3y=7-6

         {-x-2x-y+2y=1-4

         {2x-y=1

         {-3x-y=-3

           -y=-2x+1/(-1)

            y= 2x-1

 

         -3x-(2x-1)=-3

         -3x-2x+1=-3

          -5x=-2/(-5)

            x= 2/5

 

            y=2*(2/5)-1

            y=4/5 -1

            y= 4/5  - 5/5

            y= -1/5

 

d)        {6-2x-y=x+2y-3

           {-4x+3y+1=x+y+4

           {-2x-x-y-2y=-3-6

           {-4x-x+3y-y=4-1

           { -3x-3y=-9

            {-5x+2y=3

 

           -3x=-9+3y/(-3)

              x=3-y

 

           -5(3-y)+2y=3

            -15+5y+2y=3

               7y=3+15

               7y=18/7

                 y=18/7

 

               x=3-18/7

               x=21/7 -18/7

               x=3/7