Question

Rozwiąż układ równań. Dam naj...

Answer 1

A. ½(x-3) + ⅓(y+1)=1 / *6
½(x+1) - ¼(y-1)=0 / *4

3(x-3)+2(y+1)=6
2(x+1)-(y-1)=0

3x-9+2y+2=6
2x+2-y+1=0

3x+2y=13
2x-y=-3 / *2

3x+2y=13
4x-2y=-6 / +

7x=7 / :7
x=1

3*1+2y=13
2y=10 /:2
y = 5

b. ⅓(x+1)-½(y-1)=0 / *6
¾(x+2)-½(y+1)=1 /*4

2(x+1)-3(y-1)=0
3(x+2)-2(y+1)=1

2x+2-3y+3=0
3x+6-2y-2=1

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

-6x+9y=15
6x-4y=10 / +

5y=5 / :5
y=1

3x-2*1=5
3x=7 /:3
x = 2,5

c. 3/2(x-3)+2/3(y-1)=5 / *6
3/4(x-1)+4/3(y-4)=3 / *12

9(x-3)+4(y-1) = 30
9(x-1)+16(y-4)=36

9x-27+4y-4=30
9x-9+16y-64=36

9x+4y=61 / *(-1)
9x+16y=109

-9x-4y=-61
9x+16y=109 / +

12y = 48 / :12
y = 4

9x+4*4=61
9x=61-16
9x=45 / :9
x=5

d. 2/5(x+7) - 1/3(y+3)=2 / *15
1/2(x-4) + 2/3(6-y) = 3 / *6

6(x+7)-5(y+3)= 30
3(x-4)+2(6-y) = 18

6x+42-5y-15=30
3x-12+12-2y=18

6x-5y=3
3x-2y=18 / *(-2)

6x-5y=3
-6x+4y= -36 / +

-y = -33 / :(-1)
y = 33

3x - 2*33=18
3x = 18+66
3x = 84 / :3
x = 28

Answer 2

A)
1/2(x-3)+1/3(y+1)=1
1/2(x+1)-1/4(y-1)=0

1/2x-3/2+1/3y+1/3=1
1/2x+1/2-1/4y+1/4=0

1/2x+1/3y=1+3/2-1/3
1/2x-1/4y=-1/2-1/4

1/2x+1/3y=13/6
1/2x-1/4y=-3/4 /*(-1)

1/2x+1/3y=13/6
-1/2x+1/4y=3/4

7/12y=35/12 /:7/12
y=5

1/2x+1/3y=13/6
y=5

1/2x+1/3*5=13/6
y=5

1/2x+5/3=13/6
y=5

1/2x=13/6-5/3
y=5

1/2x=1/2 /:1/2
y=5

x=1
y=5

b.
1/3(x+1)-1/2(y-1)=0
3/4(x+2)-1/2(y+1)=1

1/3x+1/3-1/2y+1/2=0
3/4x+3/2-1/2y-1/2=1

1/3x-1/2y=1/3-1/2
3/4x-1/2y=1-3/2+1/2

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

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

13/12x=-5/6 /:13/12
x=-10/13

3/4x-1/2y=-1
x=-10/13

3/4*(-10/13)-1/2y=-1
x=-10/13

-15/26-1/2y=-1
x=-10/26

-1/2y=-1+15/26
x=-10/26

-1/2y=-11/26 /:(-1/2)
x=-10/26

y=11/13
x=-10/26

c.
3/2(x-3)+2/3(y-1)=5
3/4(x-1)+4/3(y-4)=3

3/2x-9/2+2/3y-2/3=5
3/4x-3/4+4/3y-16/3=3

3/2x+2/3y=5+9/2+2/3
3/4x+4/3y=3+3/4+16/3

3/2x+2/3y=61/6 /*6
3/4x+4/3y=109/12 /*(-12)

9x+4y=61
-9x-16y=-109

-12y=-48 /:(-12)
y=4

9x+4y=61
y=4

9x+4*4=61
y=4

9x+16=61
y=4

9x=61-16
x=4

9x=45 /:9
y=4

x=5
y=4

d.
2/5(x+7)-1/3(y+3)=2
1/2(x-4)+2/3(6-y)=3

2/5x+14/5-1/3y-1=2
1/2x-2+4-2/3y=3

2/5x-1/3y=2-14/5+1
1/2x-2/3y=3+2-4

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

-4/5x+2/3y=8/5
1/2x-2/3y=1

-3/10x=13/5 /:(-3/10)
x=-26/3

1/2x-2/3y=1
x=-26/3

1/2*(-26/3)-2/3y=1
x=-26/3

-13/3-2/3y=1
x=-26/3

-2/3y=1+13/3
x=-26/3

-2/3y=16/3 /:(-2/3)
x=-26/3

y=-8
x=-26/3