Question

Rozwiąż układy równań:

a)

{x-y=2

{jedna druga x - 1 = jedna czwarta y

b)

{5x-1=3y

{1,6y-2=4-2x

c)

{-x-y=2

{2(3x+y)=-20

d)

{4x+3y=54

{jedna trzecia x =4(1+ jedna ósma y )

Answer 1

a]

x-y=2

½x-1=¼y/×4

 

x=y+2

2(y+2)-4=y

 

x=y+2

2y+4-4=y

 

2y-y=0

y=0

x=0+2

x=2

b]

5x-1=3y

1,6y-2=4-2x

 

5x=1+3y

2x+1,6y=4+2

 

x=⅕+⅗y

2(⅕+⅗y)+1⅗y=6

 

⅖+⁶/₅y+⁸/₅y=6/×5

x=⅕+⅗y

 

2+6y+8y=30

 

14y=30-2

x=⅕+⅗y

 

y=28:14=2

x=⅕+⅗×2=⅕+⁶/₅=1⅖

c]

-x-y=2

2(3x+y)=-20

 

x=-y-2

6(-y-2)+2y=-20

 

x=-y-2

-6y-12+2y=-20

 

x=-y-2

-4y=-20+12

 

y=-8:-4=2

x=-2-2=-4

d]

4x+3y=54

⅓x=4(1+⅛y)

 

4x+3y=54

⅓x=4+½y

 

4x+3y=54

⅓x-½y=4/×3

 

x-1,5y=12

x=12+1,5y

 

4(12+1,5y)+3y=54

48+6y+3y=54

9y=54-48

y=6:9=⅔

 

x=12+³/₂×⅔=13