Question

Rozwiąż układy równań.

a) {x+y=3

y-3x=6

b) {x-y=6

2x+2y=3

c) {2x-y=4

-3x+4y=6

Answer 1

a) x+y=3

    y-3x=6

 

x+y=3 /*3

-3x+y=6

 

 {3x+3y=18
+{-3x+y=18
----------------

         4y=36/4

          y=9

 

x+y=3

x+9=3

3-9=x

x=-6

 

 

b) x-y=6/*2
   2x+2y=3

 

   {2x-2y=12

 + {2x+2y=3
--------------------

     4x=15/4

     x= 3,75

3,75-y=6

-y=6-3,75

-y=2,25/-1

y=-2,25

 

 

c) 2x-y=4/*4

   -3x+4y=6

 

  {8x-4y=16

+  {-3x+4y=6
---------------------

         5x=22/5

         x=4,4

 

2x-y=4

2*4,4-y=4

8,8-y=4

-y=4-8,8

-y=-4,8/*-1

y=4,8

 

 

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Answer 2

a) x+y=3

y-3x=6

y=x-3

y-3x=6

y=x-3

x-3-3x=6

-2x=9/:-2

x=-4,5

y=x-3

y=-4,5-3

x=-4,5 y=-7,5

 

b) x-y=6

2x+2y=3

x=6+y

2x+2y=3

x=6+y

2(6+y)+2y=3

x=6+y

12+2y+2y=3

x=6+y

4y=-9

y=-2 1/2

x=6+y

x=6-2 1/2

x=3 1/2 y=-2 1/2

 

2x-y=4

-3x+4y=6

-y=4-2x/*-1

y=-4+2x

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

-3x-16+8x=6

5x=22/:5

x=22/5

x=4 2/5

y=-4+2x

y=-4+2*4 2/5

y=-4+8 2/5

x=4 2/5 y=4 2,5