Mam problem z rozwiązaniem układów równań.
Proszę o wszystkie obliczenia

a)
½ (x- 4)-2 (y - 3) = 11
3 ( x - 1) - ⅓ (y + 6) = 2
b)
¾(x + 3)- (3-y) = -1
½(x - 5) + 2(y+1)= -2
c)
¼(2x - 4) - (y - 3)= -1
2(y-1) - ⅓(x-1)= 7
d)
⅓(x + 1) - 3(2y-1)=11
2(3-x) + ¼(y+1) = -4

1

Odpowiedzi

Najlepsza Odpowiedź!
2010-04-15T18:42:22+02:00
A)
½ (x- 4)-2 (y - 3) = 11
3 ( x - 1) - ⅓ (y + 6) = 2

½ (x- 4)-2 (y - 3) = 11 /*2
3 ( x - 1) - ⅓ (y + 6) = 2 /*3

x- 4- 4(y - 3) = 22
9 ( x - 1) - (y + 6) = 6

x- 4- 4y + 12 = 22
9 x - 9 - y - 6 = 6

x- 4y = 22+4-12
9 x - y = 6+6+9

x- 4y = 14 => x=14+4y (*)
9 x - y = 21
podstawiamy x do drugiego równania

9(14+4y) - y = 21
126+36y-y =21
35y=21-126
y=-105 / 35
y = - 21/7
y = - 3

z (*) x=14+4y
x=14 + 4*(-3)
x=14-12
x=2


b)
¾(x + 3)- (3-y) = -1
½(x - 5) + 2(y+1)= -2

¾(x + 3)- (3-y) = -1 / (*4)
½(x - 5) + 2(y+1)= -2 / (*2)

3(x + 3)- 4(3-y) = -4
x - 5 + 4(y+1)= -4

3x + 9- 12+4y = -4
x - 5 + 4y+ 4= -4

3x +4y = -4 -9+12
x+ 4y= -4 -4 +5

3x +4y = -1
x+ 4y= -3 => x= -4y-3 (*)

podstawiamy do 3x +4y = -1
3(-4y-3) +4y = -1
-12y-9 +4y = -1
-12y+4y = -1 +9
-8y=8
y=-1

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


c)
¼(2x - 4) - (y - 3)= -1
2(y-1) - ⅓(x-1)= 7

¼(2x - 4) - (y - 3)= -1 / *4
2(y-1) - ⅓(x-1)= 7 /*3

2x - 4 - 4(y - 3)= -4
6(y-1) - x+1= 21

2x - 4 - 4y + 12= -4
6y-6 - x+1= 21

2x - 4y = -4 +4-12
6y - x= 21 -1+6

2x - 4y = -12
6y - x= 26 => x= 6y-26

2*(6y-26) - 4y = -12
12y-52 - 4y = -12
12y-4y = 52-12
8y = 40
y= 5

x= 6y-26
x= 6*5-26
x= 30 - 26
x=4

d)
⅓(x + 1) - 3(2y-1)=11
2(3-x) + ¼(y+1) = -4

⅓(x + 1) - 3(2y-1)=11 /*3
2(3-x) + ¼(y+1) = -4 /*4

x + 1 - 9(2y-1)=33
8(3-x) +y+1 = -16

x + 1 - 18y+9=33
24-8x +y+1 = -16

x - 18y=33-9-1
-8x +y= -16 -1 -24

x - 18y=23 => x= 18y+23
-8x +y= -41

-8*(18y+23) +y= -41
-144y-184 +y= -41
-144y+y= -41+184
-143y=143
y=-1

x= 18y+23
x= 18*(-1)+23
x= -18+23
x=5