Question

!!!PomocY!!! !układy równań!

To zadanie 10 na str. 103 w podręczniku Matematyka 2.

potrzebne mi przykłady:

b) 3/5x+1/2y=2

1/2*(2x-y)=2

d)(x+y)/2-x/3=4

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

e)(3x-1)/5+(2y-3)/4=3*(y+1)/2

(x+y)/4-(3y-1)/2=(x-6y)/4

f)(3x-2)/3-(2x+9)/6=x+1/6

x+y-(-x+y)/5=1/5-0,8x

Z góry dziaa;))

Answer 1

3/5x+1/2y=2/*10

1/2*(2x-y)=2/*2

6x+5y=20

2x-y=4/*(-3)

6x+5y=20

-6x+3y=-12

_________

8y=8/:8

y=1

6x+5y=20

y=1

6x+5=20/-5

y=1

6x=15/6

y=1

x=2,5

y=1

d)

(x+y)/2-x/3=4/*6

(x-y)/2+y/3=-3/*6

3x+3y-2x=24

3x-3y+2y=-18

___________

6x=6/:6

x=1

3x+y=24

x=1

3+y=24/-3

x=1

y=21

e)

(3x-1)/5+(2y-3)/4=3*(y+1)/2 /*20

(x+y)/4-(3y-1)/2=(x-6y)/4 /4

12x-4+10y-12=3*10y+10

x+y-6y-2=x-6y

12x-18+10y=30y+10/+18

x-5y-2=x-6y/+5y

12x+10y=30y+28/-10y

x-2=x-y/-x

12x=20y+28

y=2

12x=20*2+28

y=2

12x=68/:12

y=2

x=5i2/3

f)

(3x-2)/3-(2x-9)/6=x+1/6 /*6

x-y-(-x-y)/5=1/5-0,8x /*10

6x-4-2x+9=6x+1

10x-10y+2x-2y=2-8x

4x-4=6x+1/-6x

20x-12y=2

-2x-4=1/*10

20x-12y=2

-20x-40=10

20x-12y=2

_________

12y=-28/12

y=-28/12

20x-12y=2

y=-28/12

20x+28=2/-28

20x=-26/:20

x=-26/'20

 

 

Answer 2

b) 3/5x+1/2y=2   obie strony mnoże przez 10

    1/2(2x-y)=2  obie strony mnoże przez 2

 

6x+5y=2

2x-y=4 / *5

 

6x+5y=2

4x-5y=20

 

10x=22

x=2,2

 

4x-5y=20

-5y=20-4x

y=(20-4x)/(-5)=(20-8,8)/(-5)= -2,24

 

x=2,2

y=-2,24

 

d)(x+y)/2-x/3=4  /*6

  (x-y)/2+y/3=-3 /*6

 

3(x+y)-2x=24

3(x-y)+2y=-18

 

3x+3y-2x=24

3x-3y+2y=-18

 

x+3y=24

3x-y=-18 /*3

 

x+3y=24

9x-3y=-54

 

10x=-30

x=-3

 

x+3y=24

3y=24-x

y=(24-x)/3=(24+3)/3=9

 

x=-3

y=9

 

e)(3x-1)/5+(2y-3)/4=3*(y+1)/2  /*20

(x+y)/4-(3y-1)/2=(x-6y)/4  /*4

 

4(3x-1)+5(2y-3)=30(y+1)

x+y-2(3y-1)=x-6y

 

12x-4+10y-15=30y+30

x+y-6y+2=x-6y

 

12x+10y-30y=30+19

x+y-6y+6y-x=-2

 

12x+20y=49

y=-2

 

12x=49+20y

12x=49-40

12x=9

x=3/4

 

x=3/4

y=-2