Question

Rozwiąż układy rownań metodą podstawiania:

a) {x+3y=12

{2x-y=3

b){2x-y-1=0

{x+2y-8=0

c){1/3x+2y=1

{x+y=2

Answer 1

a)

{x+3y=12

{2x-y=3

{x=12-3y

[2(12-3y)-y=3

[x=12-3y

[24-6y-y=3

[x=12-3y

[-7y=3-24

{x=12-3y

[-7y=-21  /: (-7)

{y=3

{x=12-3·3=12-9=3

{y=3

{x=3

 

b)

{2x-y-1=0

{x+2y-8=0

{2x-y-1=0

{x=8-2y

{2(8-2y)-y-1=0

{x=8-2y

{16-4y-y-1=0

{x=8-2y

{-5y=1-16

{x=8-2y

{-5y=-15  /:(-5)

{y=3

{x=8-2·3=2

 

c)

{⅓x+2y=1   /·3

{x+y=2

{x+6y=3

{x=2-y

{2-y+6y=3

{x=2-y

{5y=1  /:5

{x=2-y

{y=⅕=0,2

{x=2-0,2=1,8

 

 

 

 

Answer 2

a) {x+3y=12                          

    {2x-y=3

 

x=12-3y

2(12-3y)-y=3

24-6y-y=3/-24

-7y=-21/:(-7)

y=3

x=12-3*3=12-9=3

 

 

 

b){2x-y-1=0

   {x+2y-8=0

x=8-2y

2(8-2y)-y-1=0

16-4y-y-1=0

15-5y=o/-15

-5y=-15/:(-5)

y=3

x=8-2*3=8-6=2

 

c){1/3x+2y=1

   {x+y=2

x=2-y

1/3(2-y)+2y=1

2/3-1/3y+2y=1 /-2/3

1 i 2/3y=1/3 /:1 i 2/3

y=1/5

x=2-1/5=1 i 4/5