Question

Rozwiąż układy równań

b) x-3/4 - y+5/2 = -1,5

x-3/2 - 2y-7/3 = 1

c) 2x-5/2 - x-6y/4 = x + y/2

3x-1/10 + 2y-5/5 = 2x+y/2

w b ma wyjsc : x= -13, y= -10

w c ma wyjsc : x=-2, y=3

Answer 1

b)

x-3/4 – y+5/2 = -1,5      /*4

x-3/ 2 – 2y -7/3 = 1  /*6

 

x- 3 – 2(y+5) = -6

3(x-3) – 2*(2y-7) = 6

 

x-3 – 2y – 10 = -6

3x – 9 -4y + 14 = 6

 

x – 2y = -6 + 13

3x – 4y = 6 -5

 

x – 2y = 7   /* (-3)

3x – 4y =  1

 

-3x + 6y  =  - 21

3x – 4y =  1

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2y  =  -20  / : 2

y = -10

 

c)

2x-5/2 – x-6y/4 = x+y/2     /*4

3x-1/10 + 2y-5/5 = 2x+y/2    /* 10

 

2(2x-5) – (x-6y) = 2(x+y)

3x-1 + 2(2y-5) = 5(2x+y)

 

4x – 10 – x + 6y = 2x + 2y

3x – 1 + 4y – 10 = 10x + 5y

 

3x + 6y – 2x – 2y = 10

3x + 4y – 10x – 5y = 11

 

x + 4y = 10

-7x – y = 11  /*4

 

x+ 4y = 10

-28x – 4y = 44

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-27x = 54   / : (-27)

x =- 2

 

-2 + 4y = 10

4y = 10 + 2

4y = 12  / :4

 

y=  3

x = -2