Question

rozwiąż układy równań proszę

a) {x+2y=9

{y-1=3x

b){x-y=2

{1/2x-1=1/4y

c){-x-y=2

{2(3x+y)= -20

d){4x+3y=54

{1/3x=4(1+1/8y)

/ -ułamek

Answer 1

{x+2y=9

{y-1=3x/+1

 

{x+2y=9

{y=3x+1

 

{x+2(3x+1)=9

{y=3x+1

 

{x+6x+2=9/-2

{y=3x+1

 

{7x=7//7

{y=3x+1

 

{x=1

{y=3*1+1

 

{x=1

{y=4

 

Answer 2

a) {x+2y=9

{y-1=3x

 

{x+2y=9  |*3

{-3x+y=1

 

{3x+6y=27

{-3x+y=1

------------------

7y=28 |:7

y=4

x=9-2y

x=9-2*4

x=9-8

x=1

 

{y=4

{x=1

 

b){x-y=2

{1/2x-1=1/4y  |*4

 

{x-y=2

{2x-4=y

 

{x-y=2  |*(-1)

{2x-y=4

 

{-x+y=-2

{2x-y=4

---------------

x=2

x-y=2

-y=2-x

-y=2-2

-y=0

y=0

 

{x=2

{y=0

 

c){-x-y=2

{2(3x+y)= -20

 

{-x-y=2 |*2

{6x+2y=-20

 

{-2x-2y=4

{6x+2y=-20

-------------------

4x=-16  |:4

x=-4

 

-x-y=2

-y=2+x

-y=2+(-4)

-y=-2

y=2

 

x=-4

y=2

 

d){4x+3y=54

{1/3x=4(1+1/8y)

 

{4x+3y=54

{1/3x= 4+1/2y  |*6

 

{4x+3y=54

{2x=24+3y

 

{4x+3y=54

{2x-3y=24

----------------

6x=78 |:6

x=13

4x+3y=54

3y=54-4*13

3y=54-52

3y=2 |:3

y= 2/3

 

{x=13

{y=2/3