Question

Zadanie 10 strona 103

Rozwiąż układy równań.

b) 3/5x + 1/2y = 2

1/2(2x - y) = 2

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

x - y + 2/6 = 3

d) x+y/2 - x/3 = 4

x-y/2 + y/3 = -3

Answer 1

b)

{3/5x+1/2y=2|*10

{1/2(2x-y)=2

 

{6x+5y=20

{x-1/2y=2

 

{6x+5y=20

{x=2-1/2y

_______

6(2-1/2y)+5y=20

12-3y+5y=20

2y=20-12

2y=8|:2

y=4

____

x=2-1/2*4

x=2-2

x=0

____

c)

{x+2/5-2y=5

{x-y+2/6=3

 

{x-2y=5-2/5

{x-y=3-2/6

 

{x-2y=4 3/5

{x-y=2 4/6

x=2 4/6+y

2 4/6+y-2y=4 3/5

-y=4 3/5-2 2/3

-y=4 9/15-2 10/15

-y=1 14/15|*(-1)

y=-1 14/15

__________

x-(-1 14/15)=2 4/6

x+1 14/15=2 2/3

x=2 10/15-1 14/15

x=11/15

_______

d)

{x+y/2-x/3=4|

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

 

{x+x/3=4|*3

{x+y/3=-3|*3

 

{3x+x=12

{3x+y=-9

 

4x=12

x=3

___-

3*3+y=-9

9+y=-9

y=-9-9

y=-18

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