Zad.8 UKŁADY RÓWNAŃ METODA PRZECIWNYCH WSPÓŁCZYNNIKÓW
a)1/3x+1/2y=3
1/6x+1/2y=2 1/2
b)1/5x+y=3
3/5x-1/2y=2
c)1/2x-1/3y=-1
x+1/6y=3
d)1/2x-1/4y=1
x+1/2y=-6
Zad.9
a)1 1/2x+1 1/3y=-7
1/2x+y=-4
b)1 1/2x-1 1/5y=6
2 1/5x+1/5y=-1
c)1/2x+1/3y=5/6
1/4x-y=-3/4
Zad.10
a)0,6x+0,1y=1
0,3x-0,2y=-0,5
b)0,3x-0,4y=1,7
0,5x+0,2y=1,1
c)0,3-0,4y=0
0,4x+0,3y=-2,5
d)-0,7x+0,2y=1,4
0,2x-0,7y=-4,9
Zad.11
a)0,3x-0,2y=-3
0,4x+0,1y=7
b)0,5x+0,2y=0
0,3x+0,3y=9
c)0,2x+0,5y=2
-0,5x-0,3y=14
d)1,2x-0,5y=-7
0,4x+0,3y=-7
PLIS NA DZIŚ!!!!!!!!!!!!!!!!
Z GÓRY DZIĘKI!!!!!!!!!

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  • Roma
  • Community Manager
2010-01-21T02:43:00+01:00
Zad 8.
a)
( 1/3x+1/2y = 3 /*6
( 1/6x+1/2y = 2 1/2 /*(-6)

( 2x + 3y = 18
( - x - 3y = - 15
____________________
x = 3

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

( x = 3
( y = 4

b)
( 1/5x + y = 3 /*5
( 3/5x - 1/2y = 2 /*10

( x + 5y = 15
( 6x - 5y = 20
____________
7x = 35 /:7
x = 5

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

( x = 5
( y = 2

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

( 3x - 2y = -6
( 12x +2y = 36
____________
15x = 30 /:15
x = 2

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

( x = 2
( y = 6


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

( 2x - y = 4
( 2x + y = - 12
____________
4x = - 8 /:4
x = - 2

1/2x - 1/4y = 1
1/2*(-2) - 1/4y = 1
- 1 - 1/4y = 1
- 1/4y = 1 + 1
- 1/4 y = 2 /*(-4)
y = - 8

( x = - 2
( y = - 8

Zad.9
a)
( 1 1/2x +1 1/3y = - 7 /*6
( 1/2x + y = - 4 /*(-8)

( 9x + 8y = - 42
( - 4x - 8y = 32
_____________
5x = - 10 /:5
x = - 2

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

( x = - 3
( y = - 5

b)
( 1 1/2x - 1 1/5y = 6 /*10
( 2 1/5x + 1/5y = - 1 /*60

( 15x - 12y = 60
( 132x + 12y = - 60
________________
147x = 0 /:147
x = 0

2 1/5x + 1/5y = -1
2 1/5 * 0 + 1/5y = -1
1/5y = -1 /*5
y = - 5

( x = 0
( y = -5

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

( 6x + 4y = 10
( x - 4y = - 3
____________
7x = 7 /:7
x = 1

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

( x = 1
( y = 1

Zad.10
a)
( 0,6x + 0,1y = 1 /*2
( 0,3x - 0,2y = - 0,5

( 1,2x + 0,2y = 2
( 0,3x - 0,2y = - 0,5
__________________
1,5x = 1,5 /:1,5
x = 1

0,6x + 0,1y = 1
0,6*1 + 0,1y = 1
0,6 + 0,1y = 1
0,1y = 1 - 0,6
0,1y = 0,4 /*10
y = 4

( x = 1
( y = 4

b)
( 0,3x - 0,4y = 1,7
( 0,5x + 0,2y = 1,1 /*2

( 0,3x - 0,4y = 1,7
( x + 0,4y = 2,2
______________
1,3x = 3,9 /:1,3
x = 3

0,5x + 0,2y = 1,1
0,5*3 + 0,2y = 1,1
1,5 + 0,2y = 1,1
0,2y = 1,1 - 1,5
0,2y = - 0,4 /*5
y = - 2

( x = 3
( y = - 2

c)
( 0,3x - 0,4y = 0 /*3
( 0,4x + 0,3y = - 2,5 /*4

( 0,9x - 1,2y = 0
( 1,6x + 1,2y = - 10
_________________
2,5x = - 10 /:2,5
x = - 4

0,3x - 0,4y = 0
0,3*(- 4) - 0,4y = 0
- 1,2 - 0,4y = 0
- 0,4y = 1,2 /:(-0,4)
y = - 3

( x = - 4
( y = - 3

d)
( - 0,7x + 0,2y = 1,4 /*7
( 0,2x - 0,7y = - 4,9 /*2

( - 4,9x + 1,4y = 9,8
( 0,4x - 1,4 y = - 9,8
___________________
- 4,5x = 0 /:(-4,5)
x = 0

- 0,7x + 0,2 y = 1,4
-0,7 * 0 + 0,2y = 1,4
0,2y = 1,4 /*5
y = 7

( x = 0
( y = 7

Zad.11
a)
( 0,3x - 0,2y = - 3
( 0,4x + 0,1y = 7 /*2

( 0,3x - 0,2y = - 3
( 0,8x + 0,2y = 14
________________
1,1x = 11 /: 1,1
x = 10

0,3x - 0,2y = - 3
0,3*10 - 0,2y = - 3
3 - 0,2y = - 3
- 0,2y = - 3 - 3
- 0,2x = - 6 /: (-0,2)
y = 30

( x = 10
( y = 30

b)
( 0,5x + 0,2y = 0 /*(-3)
( 0,3x + 0,3y = 9 /*2

( -1,5x - 0,6y = 0
( 0,6x + 0,6y = 18
________________
- 0,9x = 18 /:(-0,9)
x = - 20

0,5x + 0,2y = 0
0,5*(-20) + 0,2y = 0
- 10 + 0,2y = 0
0,2y = 10 /: 0,2
y = 50

( x = - 20
( y = 50

c)
( 0,2x + 0,5y = 2 /*5
( -0,5x - 0,3y = 14 /*2

( x + 2,5y = 10
( -x - 0,6y = 28
_____________
1,9y = 38 /: 1,9
y = 20

0,2x + 0,5y = 2
0,2x + 0,5*20 = 2
0,2x + 10 = 2
0,2x = 2 - 10
0,2x = - 8 /: 0,2
x = - 40

( x = - 40
( y = 20

d)
( 1,2x - 0,5y = - 7
( 0,4x + 0,3y = - 7 /*(-3)

( 1,2x - 0,5y = - 7
( - 1,2x - 0,9y = 21
__________________
- 1,4y = 14 /:(-1,4)
y = - 10

1,2x - 0,5y = - 7
1,2x - 0,5*(-10) = - 7
1,2x + 5 = - 7
1,2x = - 7 - 5
1,2x = - 12 /: 1,2
x = - 10

( x = - 10
( y = - 10
1 1 1
2010-01-21T03:38:27+01:00
A)1/3x+1/2y=3 /*-6
1/6x+1/2y=2 1/2 /*6

-2x-3y=-18
x+3y=15
_________
-x=-3 /:(-1)
x=3

x+3y=15
3+3y=15
3y=12 /:3
y=4

x=3
y=4

b)1/5x+y=3 /*5
3/5x-1/2y=2 /*10

x+5y=15
6x-5y=20
____________
7x=35 /:7
x=5

x+5y=15
5+5y=15
5y=10 /:5
y=2

x=5
y=2

c)1/2x-1/3y=-1 /*6
x+1/6y=3 /*12

3x-2y=-6
12x+2y=36
____________
15x=30 /:15
x=2

3x-2y=-6
3*2-2y=-6
-2y=-12 /:(-2)
y=6

x=2
y=6

d)1/2x-1/4y=1 /*4
x+1/2y=-6 /*2

2x-y=4
2x+y=12
___________
4x=16 /:4
x=4

2x+y=12
2*4+y=12
y=4

Zad.9
a)1 1/2x+1 1/3y=-7
1/2x+y=-4

3/2x+4/3y=-7 /*6
1/2x+y=-4 /*(-8)

9x+8y=-7
-4x-8y=32
___________
5x=25 /:5
x=5

-4x-8y=32
-4*5-8y=32
-8y=52 /:(-8)
y=-6,5

x=5
y=-6,5

b)1 1/2x-1 1/5y=6
2 1/5x+1/5y=-1

3/2x-6/5y=6 /*10
11/5x+1/5y=-1 /*60

15x-12y=60
132x+12y=-60
_______________
147x=0 /:147
x=0

15x-12y=60
15*0-12y=60
-12y=60 /:(-12)
y=-5

x=0
y=-5


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

6x+4y=10
x-4y=-3
__________
7x=7 /:7
x=1

6x+4y=10
6*1+4y=10
4y=4 /:4
y=1

x=1
y=1


Zad.10
a)0,6x+0,1y=1 /*2
0,3x-0,2y=-0,5

1,2x=0,2=2
0,3x-0,2y=-0,5
_________________
1,5x=1,5 /:1,5
x=1

0,3x-0,2y=-0,5
0,3*1-0,2y=-0,5
-0,2y=-0,8 /:(-0,2)
y=4

x=1
y=4

b)0,3x-0,4y=1,7
0,5x+0,2y=1,1 /*2

0,3x-0,4y=1,7
x+0,4y=2,2
______________
1,3x=3,9 /:1,3
x=3

0,5x+0,2y=1,1
0,5*3+0,2y=1,1
1,5+0,2y=1,1
0,2y=1,1-1,5
0,2y=-0,4 /*5
y=-2

x=3
y=-2

c)0,3-0,4y=0 /*3
0,4x+0,3y=-2,5 /*4

0,9x-1,2y=0
1,6x+1,2y=-10
_________________
2,5x=-10 /:2,5
x=-4

0,3x-0,4y=0
0,3*(-4)-0,4y=0
-1,2-0,4y=0
-0,4y=1,2 /:(-0,4)
y=-3

x=-4
y=-3

d)-0,7x+0,2y=1,4 /*7
0,2x-0,7y=-4,9 /*2

-4,9x+1,4y=9,8
0,4x-1,4y=-9,8
___________________
-4,5x=0 /:(-4,5)
x=0

-0,7x+0,2y=1,4
-0,7*0+0,2y=1,4
0,2y=1,4/*5
y=7

x=0
y=7

Zad.11
a)0,3x-0,2y=-3
0,4x+0,1y=7/*2

0,3x-0,2y=-3
0,8x+0,2y=14
________________
1,1x=11/: 1,1
x=10

0,3x-0,2y=-3
0,3*10-0,2y=-3
3-0,2y=-3
-0,2x=-6 /:(-0,2)
y=30

x=10
y=30

b)0,5x+0,2y=0 /*(-3)
0,3x+0,3y=9 /*2

-1,5x-0,6y=0
0,6x+0,6y=18
________________
-0,9x=18 /:(-0,9)
x=-20

0,5x+0,2y=0
0,5*(-20)+0,2y=0
0,2y=10 /:0,2
y=50

x=-20
y=50

c)0,2x+0,5y=2 /*5
-0,5x-0,3y=14 /*2

x+2,5y=10
-x-0,6y=28
_____________
1,9y=38 /:1,9
y=20

0,2x+0,5y=2
0,2x + 0,5*20=2
0,2x+10=2
0,2x=-8 /: 0,2
x=-40

x=-40
y=20

d)1,2x-0,5y=-7
0,4x+0,3y=-7 /*(-3)

1,2x-0,5y=-7
-1,2x-0,9y=21
__________________
-1,4y=14 /:(-1,4)
y =-10

1,2x-0,5y=-7
1,2x-0,5*(-10)=-7
1,2x+5=-7
1,2x=-12 /:1,2
x=-10

x=-10
y=-10