Question

Rozwiąż układ równań metoą podstawiania i sprawdź otrzymane rozwiązanie.

{

{

*( weźcie to za jedną klamre)

a)

{2x+y=8

{x=3

b)

{x-y=6

{y=-1

c)

{3x-2y=6

{x=4

d)

{3x+y=10

{y=2x

e)

{-x-3y=5

{y=-2x

f)

{4x-y=6

{y=x

g)

{x+y=7

{x-y=1

h)

{2x-y=4

{x+y=11

i)

{x-2y=-3

{2x+3y=8

Answer 1

a){2x+y=8

{x=3

2*3+y=8

x=3

6+y=8

x=3

y=8-6

x=3

y=2

x=3

 

b) x-y=6

y=-1

x-(-1)=6

y=-1

x+1=6

y=-1

x=6-1

y=-1

x=5

y=-1

 

c) {3x-2y=6

{x=4

3*4-2y=6

x=4

12-2y=6

x=4

-2y=6-12

x=4

 

-2y=-6/:(-2)

x=4

y=3

x=4

 

c) {3x+y=10

{y=2x

3x+2x=10

y=2x

5x=10/:5

y=2x

x=2

y=2*2

x=2

y=4

 

e){-x-3y=5

{y=-2x

-x-3*(-2x)=5

y=-2x

-x+6x=5

y=-2x

5x=5/:5

y=-2x

x=1

y=-2*1

x=1

y=-2

 

f){4x-y=6

{y=x

4x-x=6

y=x

3x=6/:3

y=x

x=2

y=2

 

g) x+y=7

{x-y=1

x=7-y

7-y-y=1

x=7-y

7-2y=1

x=7-y

-2y=1-7

x=7-y

-2y=-6/:(-2)

x=7-y

y=3

x=7-3

y=3

x=4

 

h){2x-y=4

{x+y=11

2*(11-y)-y=4

x=11-y

22-2y-y=4

x=11-y

22-3y=4

x=11-y

-3y=4-22

x=11-y

-3y=-18/:(-3)

x=11-y

y=6

x=11-6

y=6

x=5

 

i){x-2y=-3

{2x+3y=8

x=-3+2y

2*(-3+2y)+3y=8

x=-3+2y

-6+4y+3y=8

x=-3+2y

7y=8+6

x=-3+2y

7y=14/:7

x=-3+2y

y=2

x=-3+2*2

y=2

x=-3=4

y=2

x=1

 

 

 

 

 

 

 

Answer 2

a) [2x+y=8

[ x=3

 

[y=-2x+8

[x=3

 

b) [x-y=6

[y=-1

 

[-y=-x+6/*(-1)

[y=-1

 

[y=x-6

[y=-1

 

c)[3x-2y=6

[x=4

 

[-2y=-3x+6/:(-2)

[x=4

 

[y=1,5x-3

[x=4

 

d)[3x+y=10

[y=2x

 

[y=-3x+10

[y=2x

 

e) [-x-3y=5

[y=-2x

 

[-3y=x+5/:(-3)

[y=-2x

 

[y=-jednatrzecia x - piectrzecich

[y=-2x

 

f)[4x-y=6

[y=x

 

[-y=-4x=6/*(-1)

[y=x

 

[y=4x-6

[y=x

 

g)[x+y=7

[x-y=1

 

[y=-x+7

[-y=-x+1/*(-1)

 

[y=-x+7

[y=x-1

 

h)[2x-y=4

[x+y=11

 

[-y=-x+4/*(-1)

[y=-x+11

 

[y=x-4

[y=-x+11

 

i) [x-2y=-3

[2x+3y=8

 

[-2y=-x-3/:(-2)

[3y=-2x+8/:(3)

 

[y=0,5x+1,5

[y=dwietrzecie x + osiem trzecich

 

 

Prosze Bardzo ;)