Rozwiąż układy równań ;

1) x-4y=-3
3x-2y=1

2) 5x-y=3
x-y=3

3) 2x-3y=4
3x-y=6

4) x-3 = y-2
------ ------
5 3
3x+0,5y=10

5) x+y=0
2x+3y=1

6) 2x+y=2
x-2y=11

7)1-0,3(y-2)=0,2(x+1)
y-3 + 4x+9 =15
---- -----
4 20

8)y-x=3
1/2y-1/2x=3

Proszę rozwiążcie wszystkie ;)
Za wszystkie daje 34 bo nie mam więcej ;)

3

Odpowiedzi

2010-02-03T19:37:42+01:00
1) {x=-3+4y
3(-3+4y)-2y=1
{x=-3+4y
-9+12y-2y=1
{x=-3+4y
10y=10||10
{x=-3+4y
y=1
{x=-3+4*1
y=1
{x=1
y=1

2) {5x-y=3
x-y=3
{5x-y=3
x=3+y
{5(3+y)-y=3
x=3+y
{15+5y-y=3
x=3+y
{4y=3-15
x=3+y
{4y=-12||4
x=3+y
{y=-3
x=3+y
{y=-3
x=3+(-3)
{y=-3
x=0

3) {2x-3y=4
3x-y=6|-3
{2x-3y=4
-9x+3y=-18
-----------------
-7x=-14||-7
x=2
{x=2
3*2-y=6
-y=6-6||-1
y=0

4) x-3 = y-2
------ ------|15 [3x-9=5y-10] [3x-5y=-1]
5 3
3x+0,5y=10|2
{3x-5y=-1|-2
6x+y=20
{-6x+10y=2
6x+y=20
----------------
11y=22||11
y=2
{y=2
3x-10=-1
{y=2
3x=9||3
{y=2
x=3


5) {x+y=0|-2
2x+3y=1
{-2x-2y=0
2x+3y=1
------------
y=1
{y=1
x+1=0
x=-1

6) {2x+y=2|2
x-2y=11
{4x+2y=4
x+2y=11
------------
5x=15||5
x=3
{x=3
y+3*2=2
{x=3
y=2-6
{x=3
y=-4

8){y-x=3
1/2y-1/2x=3||-0.5
{y-x=3
-y+x=-6
----------
0=-3
sprzeczne

2010-02-03T19:45:15+01:00
1)
x-4y=-3
3x-2y=1

x=-3+4y
3*(-3+4y)-2y=1
-9+12y-2y=1
10y=10
y=1
x-4=-3
x=1
odp x=1, y=1

2)
5x-y=3
x-y=3

x=3-y
5*(3-y)-y=3
15-5y-y=3
-6y=-12
y=2
x=3-2
x=1
odp x=1, y=2

3)
2x-3y=4
3x-y=6

y=3x-6
2x-3*(3x-6)=4
2x-9x+18=4
-7x=-14
x=2
6-y=6
y=0
odp x=2, y=0

5)
x+y=0
2x+3y=1

x=-y
-2y+3y=1
y=1
x+1=0
x=-1
odp x=-1, y=1

6)
2x+y=2
x-2y=11

2x+y=2/*2
x-2y=11

4x+2y=4
x-2y=11

4x+2y+x-2y=15
5x=15
x=3
3-2y=11
y=-4
odp x=3, y=-4

8)
y-x=3
1/2y-1/2x=3

równanie sprzeczne

  • Roma
  • Community Manager
2010-02-03T20:10:42+01:00
1)
( x - 4y = -3 /*(-3)
( 3x - 2y = 1

( -3x + 12y = 9
( 3x - 2y = 1
_____________
10y = 10 /:10
y = 1

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

( x = 1
( y = 1


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

( 5x - y = 3
( -x + y = -3
___________
4x = 0 /:4
x = 0

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

( x = 0
( y = - 3

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

( 2x - 3y = 4
( -9x + 3y = -18
______________
-7x = -14 /:(-7)
x = 2

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

( x = 2
( y = 0


4)
( x - 3 / 5 = y - 2 / 3 /*15
( 3x + ½*y = 10 /*2

( 3(x - 3) = 5(y - 2)
( 6x + y = 20

( 3x - 9 = 5y - 10
( 6x + y = 20

( 3x - 5y = - 10 + 9
( 6x + y = 20

( 3x - 5y = - 1
( 6x + y = 20 /*5

( 3x - 5y = - 1
( 30x + 5y = 100
______________
33x = 99 /:33
x = 3

6x + y = 20
6*3 + y = 20
18 + y = 20
y = 20 - 18
y = 2

( x = 3
( y = 2


5)
( x + y = 0 /*(-2)
( 2x + 3y = 1

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

x + y = 0
x + 1 = 0
x = -1

( x = -1
( y = 1

6)
( 2x + y = 2
( x - 2y = 11 /*(-2)

( 2x + y = 2
( -2x + 4y = -22
______________
5y = -20 /:5
y = -4

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

( x = 3
( y = -4

7)
( 1 - 0,3(y - 2) = 0,2(x + 1)
( y - 3 / 4 + 4x + 9 / 20 = 15

( 1 - 0,3y + 0,6 = 0,2x + 0,2
( y - 3 / 4 + 4x + 9 / 20 = 15 /*20

( -0,2x - 0,3y = 0,2 - 1 - 0,6
( 5(y - 3) + 4x + 9 = 300

( -0,2x - 0,3y = -1,4 /*10
( 5y - 15 + 4x + 9 = 300

( -2x - 3y = -14 /*2
( 4x + 5y = 300 + 15 - 9

( -4x - 6y = -28
( 4x + 5y = 306
_____________
-y = 278 /*(-1)
y = -278

4x + 5y = 306
4x + 5*(-278) = 306
4x - 1390 = 306
4x = 306 + 1390
4x = 1696 /:4
x = 424

( x = 424
( y = -278

8)
( y - x = 3
( ½*y - ½*x = 3 /*(-2)

( -x + y = 3
( x - y = -6
__________
0 = - 3

Układ sprzeczny, zbiorem rozwiązań jest zbiór pusty.