Question

Rozwiąż układ równań stosując metodę podstawiania:

2) 1/2

3) x =2y

2x+5y=90

4) x=3y

x+5=2(y+5)

5) x+y=13

10y+x=9+10x+y

6) 2a+2b=34

a-3=b+2

Answer 1

2)

1/2x+2y=8
x/y=4  /·y

 

1/2x+2y = 8

x = 4y

 

1/2·4y+2y = 8

x = 4y

 

2y+2y = 8

x = 4y

 

4y = 8  /:4

x = 4y

 

y = 2

x = 4·2

 

y = 2

x = 8

 

3)

x =2y

2x+5y=90

 

x = 2y

2·2y+5y = 90

 

x = 2y

4y+5y = 90

 

x = 2y

9y = 90  /:9

 

x = 2y

y = 10

 

x = 2·10

y = 10

 

x = 20

y = 10

 

4)

x=3y

x+5=2(y+5)

 

x = 3y

x+5 = 2y+10

 

x = 3y

x-2y = 10-5

 

x = 3y

3y-2y = 5

 

x = 3y

y = 5

 

x = 3·5

y = 5

 

x = 15

y = 5

 

5)

x+y=13

10y+x=9+10x+y

 

x = 13-y

10y-y+x-10x = 9

 

x = 13-y

9y-9x = 9

 

x = 13-y

9y-9(13-y) = 9

 

x = 13-y

9y-117+9y = 9

 

x = 13-y

9y+9y = 9+117

 

x = 13-y

18y = 126  :18

 

x = 13-y

y = 7

 

x = 13-7

y = 7

 

x = 6

y = 7

 

6)

2a+2b=34

a-3=b+2

 

2a+2b = 34

a-b = 2+3

 

2a+2b = 34

a = 5+b

 

2(5+b)+2b = 34

a = 5+b

 

10+2b+2b = 34

a = 5+b

 

2b+2b = 34-10

a = 5+b

 

4b = 24  /:4

a = 5+b

 

b = 6

a = 5+6

 

b = 6

a = 11