Rozwiąż metodą przeciwnych współczynników poniższe układy równań
a) 5x - 4y = 1
5x + 2y = 4
b) 4x + 3y = -3
8x + 5y = -4
c) 4x + 3y = -3
8x + 5y = -4
d) 2(x + 3) - 3 (y-2) = -4
3( x + y+2) = 2(2x + y + 6)
e) (x - 2) do potęgi 2 + 2y = (x-1) do potęgi 2 + y - 1
2x = 3y



PILNE!!! Na dzisiaj !

2

Odpowiedzi

Najlepsza Odpowiedź!
2010-03-01T16:24:19+01:00
A) 5x - 4y = 1 /* (-1)
5x + 2y = 4

-5x + 4y = -1
5x + 2y = 4
dodajesz stronami:
6y= 3 /:6
y = 1/2
znasz juz y, więc podstawiasz go do dowolnego równania, np:
5x - 4 *1/2 = 1
5x - 4/2 =1
5x= 1+ 2
5x= 3 /:5
x=3/5
b) 3y - 5x = 5
4(x+1) = 3(y-1)

3y - 5x = 5
4x +4 = 3y - 3

- 5x +3y = 5
4x - 3y = -7
dodajesz stronami:
-x = -2 /*(-1)
x= 2

3y - 5*2 = 5
3y = 5 + 10
3y = 15 /:3
y = 5

c) 4x + 3y = -3 /*(-2)
8x + 5y = -4

-8x - 6y = 6
8x + 5y = -4

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

8x + 5*(-2) = -4
8x = -4 +10
8x= 6 / :8
x = 3/4

d)2x- 10 + 3y-3 = 5x- 20 - 4y

x - 1 y + 3
___ + ____= 2 /*30
6 5

2x-5x +3y+4y = 10 +3 -20
5(x-1) + 6(y+3) = 60

-3x +7y =-7
5x- 5 + 6y +18 =60

-3x +7y =-7 /*5
5x +6y = 47 /*3

-15x + 35y = -35
15x + 18y = 141

53y= 106 /:53
y=2

-3x +7*2 =-7
-3x = -7- 14
-3x = -21 /:(-3)
x= 7

e) x do potegi 2 -4x +4 +2 y = x do potegi 2 - 2x +1 +y -1
2x=3y

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

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

-2y= -4 /:(-2)
y = 2

2x=3*2
2x= 6 /: 2
x =3
20 4 20
2010-03-01T16:31:49+01:00
A) 5x - 4y=1
5x +2y=4 / *2

5x - 4y= 1
10x + 4y=8

15x = 9 /:15
x = 0,6

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

5x - 4y=1
-5x - 2y = -4
- 6y = -3 /:(-6)
y = 0,5


b)4x + 3y = -3 /* (-2)
8x + 5y = -4

-8x - 6y= 6
8x + 5y = -4

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

4x + 3y = -3 /* (-5)
8x + 5y = -4 / *3

- 20x - 15y = 15
24x + 15y = -12
4x = 3 / : 4
x = 0,75


c) 4x + 3y = -3 /* (-2)
8x + 5y = -4

-8x - 6y= 6
8x + 5y = -4

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

4x + 3y = -3 /* (-5)
8x + 5y = -4 / *3

- 20x - 15y = 15
24x + 15y = -12
4x = 3 / : 4
x = 0,75

d) 2(x + 3) - 3 (y-2) = -4
3( x + y+2) = 2(2x + y + 6)

2x + 6 - 3y + 6= -4
3x + 3y + 6 = 4x + 2y + 12

2x - 3y = -4 - 6 - 6
3x + 3y - 4x - 2y= 12- 6

2x - 3y = - 16
-x + y = 6 / * 2

2x - 3y = - 16
-2x +2y = 12
-y = -4 /: (-1)
y = 4


2x - 3y = - 16
-x + y = 6 / * 3

2x - 3y = - 16
-3x + 3y = 18

-x = 2 /:(-1)
x= -2















1 5 1