Rozwiąż układ równań metodą przeciwnych współczynników i sprawdz otrzymane rozwiązanie. ZA 6 PRZYKŁADÓW 100 PKT .

a) KLAMRA 3x + 2y = 5
2x + 2y = 2

b) KLAMRA x + 4y = 11
2x + 5y = 10

c) KLAMRA 4x + 5y = -4
6x + 7y = -6

d) KLAMRA 2x - 11y = 73
3x - 4y = 47

e) KLAMRA -2x + 5y = -10
7x - 4y = 8

f) KLAMRA 9x + 8y = 1
5x - 6y = 11

3

Odpowiedzi

2010-01-13T17:55:40+01:00
A)
3x + 2y = 5
2x + 2y = 2 / * (-1)

3x + 2y = 5
-2x - 2y = -2
+____________
x=3

3*3+2y=5
y=-2

b)
x + 4y = 11 / * (-2)
2x + 5y = 10

-2x - 8y = -22
2x + 5y = 10
+____________
-3y= -12
y= 4

2x + 5*4 = 10
x=-5


c)
4x + 5y = -4 / * (-3)
6x + 7y = -6 / *2

-12x - 15y = 12
12x + 14y = -12
+_____________
y=0

4x +5*0 = -4
x= -1


d)
2x - 11y = 73 / * (-3)
3x - 4y = 47 / *2

-6x + 33y = -219
6x - 8y = 94
+____________
25y = -125
y= -5

3x - 4*(-5) = 47
x= 9


e)
-2x + 5y = -10 / *7
7x - 4y = 8 / *2

-14x + 35y = -70
14x - 8y = 16
+____________
27y = -54
y = -2

-2x +5*(-2) = -10
x= 0


f)
9x + 8y = 1 / *3
5x - 6y = 11 / *4

27x + 24y = 3
20x - 24y = 44
+__________
47x = 47
x=1

5 - 6y = 11
y= -1
2 5 2
Najlepsza Odpowiedź!
2010-01-13T18:00:45+01:00
A) 3x + 2y = 5
2x + 2y = 2 /*(-1)

3x+2y=5
-2x-2y=-2
_________
x=3
3*3+2y=5
2y=5-9
2y=-4
y=-2

spr. 3*3+2*(-2)=5
9-4=5

b)x + 4y = 11 / *(-2)
2x + 5y = 10

-2x-8y=-22
2x+5y=10
_________
-3y=-12
y=4
2x+ 5*4=10
2x+20=10
2x=-10
x=-5

spr. -5+4*4=11
-5+16=11

c)4x + 5y = -4 /*3
6x + 7y = -6 /*(-2)

12x+15y=-12
-12x-14y=12
___________
y=0
4x+0=-4
x=-1

spr. 4*(-1)+5*0=-4
-4=-4

d) 2x - 11y = 73 / *3
3x - 4y = 47 / *(-2)

6x-33y=219
-6x+8y=-94
__________
-25y=125
y=-5
2x-11*(-5)=73
2x+55=73
2x=18
x=9

spr. 3*9 -4*(-5)=47
27+20=47


e) -2x + 5y = -10 /*7
7x - 4y = 8 / *2

-14x+35y=-70
14x-8y=16
_________
27y=-54
y=2
-2x+5*2=-10
-2x+10=-10
-2x=-20
x=10

spr. -2*10+5*2=-10
-20+10=-10

f) 9x + 8y = 1 / * (-5)
5x - 6y = 11 / 8*9

-45x-40y=-5
45x-54y=99
__________
-94y=-94
y=1
9x+8=1
9x=-7
x=-7/9

spr. 9*(-7/9) + 8*1=1
-7+8=1

4 5 4
2010-01-13T20:13:41+01:00
A)
3x + 2y = 5
2x + 2y = 2 |*-1

3x + 2y = 5
-2x - 2y = -2

x = 3
3 * 3 + 2y = 5
2y = 5 - 9
2y = -4
y = -2



b)
x + 4y = 11 |*-2
2x + 5y = 10

-2x - 8y = -22
2x + 5y = 10

-3y = -12
y = 4
2x + 5 * 4 = 10
2x + 20 = 10
2x = -10
x = -5


c)
4x + 5y = -4 |*3
6x + 7y = -6 |*-2

12x + 15y = -12
-12x - 14y = 12

y = 0
4x + 0 = -4
x = -1



d)
2x - 11y = 73 |*3
3x - 4y = 47 |*-2

6x - 33y = 219
-6x + 8y = -94

-25y = 125
y = -5
2x - 11*-5 = 73
2x + 55 = 73
2x = 18
x = 9



e)
-2x + 5y = -10 | *7
7x - 4y = 8 | *2

-14x + 35y = -70
14x - 8y = 16

27y = -54
y = 2
-2x + 5* 2= -10
-2x + 10 = -10
-2x = -20
x = 10



f)
9x + 8y = 1 |* -5
5x - 6y = 11 |8*9

-45x - 40y = -5
45x - 54y = 99

-94y = -94
y = 1
9x + 8 = 1
9x = -7
x = -7/9

1 5 1