Odpowiedzi

2010-02-21T18:18:56+01:00
A)
{3x+y= -5/*(-3)
{2x+3y=6

{-9x-3y=15
{2x+3y=6
------------
-7x=21/:(-7)
x=-3

2*(-3)+3y=6
3y=6+6
3y=12/:3
y=4

B)
{3x-2y=8,5/*3
{3y-2x=-9/*2

{9x-6y=25,5
{-4x+6y=-18
---------------
5x=7,5/:5
x=1,5

-4*1,5+6y=-18
6y=-18+6/:6
y=-2

C)
{2(x+2y)-5=-7
{6y-5x+1=6

{2x+4y=-7+5
{6y-5x=6-1

{2x+4y=-2/*5
{-5x+5y=5/*2

{10x+20y=-10
{-10x+10y=10
---------------
30y=0
y=0

10x+20*0=-10
10x=-10/:10
x=-1

D)
{-3(2+y)=6x-30
{2y-5(x+y)=-9

{-6-3y=6x-30
{2y-5x-5y=-9

{-3y-6x=-30+6
{-3y-5x=-9

{-3y-6x=-24
{-3y-5x=-9/*(-1)

{-3y-6x=-24
{3y+5x=9
--------------
-x=--15/:(-1)
x=15

3y+5*15=9
3y=9-75
3y=-66/:3
y=-22

E)
{2(2y-x)=3y+x+8
{-5(x+y)=-4x-y+7

{4y-2x=3y+x+8
{-5x-5y=-4x-y+7

{4y-2x-3y-x=8
{-5x-5y+4x+y=7

{y-3x=8
{-x-4y=7/*(-3)

{y-3x=8
{12y+3x=-21
----------------
13y=-13/:13
y=-1

-1-3x=8
-3x=8+1
-3x=9/:(-3)
x=-3

F)
{2(x+y)+3=3(x+2y)-7
-(x+2y)=6y+2x-10

{2x+2y+3=3x+6y-7
{-x-2y=6y+2x-10

{2x+2y-3x-6y=-7-3
{-x-2y-6y-2x=-10

{-x-4y=-10/*(-2)
{-3x-8y=10

{2x+8y=20
{-3x-8y=10
--------------
-x=30/:(-1)
x=30

2*30+8y=20
8y=20-60
8y=-40/:8
y=-5




2010-02-21T18:19:28+01:00
Rozumiem, że to są układy równań... Zrobię to metodą podstawiania.
więc:

a)
3x+y= -5 |*(-3)
2x+3y=6

-9x-3y=15
2x+3y=6

-7x=21 |/(-7)
x=-3

x=-3
2x+3y=6

x=-3
-6+3y=6

x=-3
3y=0

x=-3
y=0

b)
3x-2y=8,5 |*2
3y-2x=-9 |*3

6x-4y=17
-6x+9y=-27

5y=10 |/5
y=2

y=2
3y-2x=-9

y=2
6-2x=-9

y=2
-2x=-15

y=-2
x=7 i1/2

c)
2(x+2y)-5=-7
6y-5x+1=6

2x+4y=-2 |*3
6y-5x=5 |*(-2)

6x+12y=-6
10x-12y=-10

16x=-16
x=-1

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

x=-1
4y=-4

x=-1
y=-1

d)
-3(2+y)=6x-30
2y-5(x+y)=-9

-6-3y=6x-30
2y-5x-5y=-9

-3y-6x=-24 |*(-1)
-3y-5x=-9

3y+6x=24
-3y-5x=-9

x=15

x=15
-3y-5x=-9

x=15
-3y=66 |/(-3)

x=15
y=-22

e)
2(2y-x)=3y+x+8
-5(x+y)=-4x-y+7

4y-2x=3y+x+8
-5x-5y=-4x-y+7

y-3x=8
-4y-x=7 |*(-3)

y-3x=8
12y+3x=-21

13y=13

y=1

y=1
y-3x=8

y=1
-3x=7

y=1
x=-2 i1/3

f)
2(x+y)+3=3(x+2y)-7
-(x+2y)=6y+2x-10

2x+2y+3=3x+6y-7
-x-2y=6y+2x-10

-x-4y=-10 |*(-3)
-3x-8y=-10

3x+12y=30
-3x-8y=-10

20y=20
y=1

y=1
-3x-8y=-10

y=1
-3x=-2

y=1
x=2/3