Question

Rozwiąż układy równań metodą podstawiania: c) 3m+n=9 2m-5n=-11 d) 4a-2=b 3a+7b=1,5 e) 5x=4-2y 4x+y=3 f) 6x-3y=9 x+5y=-9,5

Answer 1

: c) 3m+n=9

2m-5n=-11

 

n = 9-3m

2m-5n = -11

 

2m-5(9-3m) = -11

2m-45 +15m=-11

17m=34

m=2, n=3

 

3a+7b=1,5

4a-2=b

 

3a +7(4a-2) =1,5

3a+28a-14=1,5

31a  = 15,5

a=1/2  , b=0

 

e) 5x=4-2y

4x+y=3

 

5x+2y=4

y=3-4x

 

5x+2(3-4x)=4

5x+6-8x=4

-3x=-2

x=2/3,  y=1/3

 

 

6x-3y=9

x+5y=-9,5

 

6x-3y=9

x=-9,5-5y

 

6(-9,5-5y)-3y=9

-57-30y-3y=9

-33y=66

y=-2,  x=0,5

 

 

 

 

 

Answer 2

3m+n=9

2m-5n=-11

{n=9-3m

{2m-5(9-3m)=-11

{n=9-3m

{2m-45+15m=-11

{n=9-3m

{17m=34

{n=9-3m

{m=2

{n=9-3·2=3

{m=2

{n=3

 

d)4a-2=b

3a+7b=1,5

{b=4a-2

{3a+7(4a-2)=1,5

{b=4a-2

{3a+28a-14=1,5

{b=4a-2

{31a=15,5

{b=4a-2

{a=½

{b=4·½-2=0

{a=½

{b=0

e)

5x=4-2y

4x+y=3

{5x+2y=4

{y=3-4x

{5x+2(3-4x)=4

{y=3-4x

{5x+6-8x=4

{y=3-4x

{-3x=-2

{y=3-4x

{x=⅔

{y=3-4·⅔=3-2⅔=⅓

{x=⅔

{y=⅓

 

f)6x-3y=9

x+5y=-9,5

{6x-3y=9

{x=-9,5-5y

{6(-9,5-5y)-3y=9

{x=-9,5-5y

{-57-30-3y=9

{x=-9,5-5y

{-33y=66

{x=-9,5-5y

{y=-2

{x=-9,5-5·(-2)=-9,5+10=½

{y=-2

{x=½