Question

Rozwiąż układy równań dowolną metodą. b) {6x-9y=6 {8x+5y= 7/3

c) {5-y=7 {2(x-1)=2y

d){4(x-2)-y=2 {2x-4y=8

e){a/3 + b/5 = 7 {a/4 - b/5 = 0

f) {k/3 + l/4 = 1 { k/4 + l/4 = 1

h) {5x-5y= 2,5 {7y+3x= -14,5

i) {20/y - 12/x = 1 { 10/y + 8/x =4

Answer 1

 b)

6x-9y=6             

8x+5y= 7/3   /*3     

 

6x-9y = 6    /*(-4)

24x + 15y = 7

 

-24x + 36y = -24

24x + 15y = 7

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

51y = -17    /: 51

y = -17/51

y = -1/3

 

6x – 9 * (-1/3) = 6

6x  + 3 = 6

6x = 6-3

6x = 3  /:6

x = 3/6

 

x = ½

y = - 1/3

 

c)

5-y=7

2(x-1)=2y

 

y = 5-7

2x – 2 = 2y

 

y = -2

2x = 2 + 2*(-2)

 

y = -2

2x =  -2   /:2

 

y = -2

x = -1

 

d)

4(x-2)-y=2

2x-4y=8

 

4x – 8 – y = 2

2x – 4y = 8

 

4x – y = 2 +8

2x – 4y = 8   / * (-2)

 

4x – y = 10

-4x + 8y = -16

----------------------- 

7y = -6   /:7

y = -6/7

 

2x – 4 * (-6/7) = 8

2x = 8 – 24/7

2x = 32/7   /:2

x = 32/14

y = - 6/7

4(x-2)-y=2    

2x-4y=8       

 

e)

a/3 + b/5 = 7    /* 15

a/4 - b/5 = 0    / *20

 

5a + 4b = 105

5a – 4b = 0

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

10a = 105    /:10

a = 10,5

 

5*10,5 – 4b = 0

4b = 52,5   /:4

 

b = 13,125

a = 10,5

 

f)

k/3 + l/4 = 1    /*12

k/4 + l/4 = 1    /*4

 

4k + 3I = 12

k + I = 4    /*(-4)

 

4k +3I = 12

-4k – 4I = -16

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

-I = -4    /* (-1)

I = 4

 

k + 4 = 4

k = 4 – 4

 

k = 0

I = 4

 

h)

5x-5y= 2,5    /* 1,4   

7y+3x= -14,5        

 

-7y + 7x =  3,5

7y + 3x = -14,5

----------------------- 

10x =  - 11   /:10

x = - 1,1

 

5 *(-1,1) -5y = 2,5

-5y = 2,5 + 5,5

-5y = 8  /: (-5)

y = - 8/5

 

y = -1,6

x = - 1,1

 

i)

20/y - 12/x = 1      /*xy           x,y ≠0

10/y + 8/x =4    / * xy

 

20x – 12y = xy

10x + 8 y = 4xy   / * (-2)

 

20x – 12y = xy

-20x – 16y = -8xy

 

-28y = - 7xy    / : (-7y)

x = 28/7

x = 4

 

20 * 4 – 12y = 4 y

4y  + 12y = 80

 

16y = 80   /:16

 

y = 5

x = 4