Zadanie:
Doprowadź każde z równań do najprostszej postaci i rozwiąż układ równań metodą podstawiania.

a) x-3(y-3x)=3x-4
2(2x-y)=4

b) 3(2+y)= -2x-1
2(x+1)=2-10y

c) -2(x+2)+3y= -y-4
5(x-1)=x-3(x+y)-1

d) 2(x-4y)+4x-y
4x-4y= -8

Proszę o pomoc.
Daje naj.

3

Odpowiedzi

2010-03-12T16:49:13+01:00
A) x-3(y-3x)=3x-4
2(2x-y)=4

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

7x-3y=-4
4x-2y=4

7x=3y-4 /7
x=3/7y-4/7

4(3/7y-4/7)-2y=4
12/7y-16/7-2y=4
-2/7y=6 2/7 /-2/7
y=-16

4x-2*-16=4
4x+32=4
4x=-28 /4
x=-7


b) 3(2+y)= -2x-1
2(x+1)=2-10y

6+3y=-2x-1
2x+2=2-10y

3y+2x=-7
10y+2x=0

x=-5y

3y+2*(-5y)=-7
3y-10y=-7
-7y=-7 /-7
y=1

x=-5*1
x=-5


c) -2(x+2)+3y= -y-4
5(x-1)=x-3(x+y)-1

-2x-4+3y=-y-4
5x-5=x-3x-3y-1

-2+4y=0
7x+3y=4

4y=2
y=1/2

7x+3*1/2=4
7x+3/2=4
7x=2.5
x=2.8


d) 2(x-4y)+4x-y
4x-4y= -8

2x-8y+4x-y=0
4x-4y=-8

6x-9y=0
x-y=-2

x=y-2

6(y-2)-9y=0
6y-12-9y=0
-3y=12 /-3
y=-4

x=-4-2
y=-6
9 4 9
2010-03-12T17:16:34+01:00
A)
x-3(y-3x)=3x-4
2(2x-y)=4

x-3y+9x=3x-4
4x-2y=4 /:(-2)

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

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

7x-3(-2+2x)=-4
y=-2+2x

7x+6-6x=-4
y=-2+2x

7x-6x=-4-6
y=-2+2x

x=-10
y=-2+2×(-10)

x=-10
y=-22

b)
3(2+y)=-2x-1
2(x+1)=2-10y

6+3y=-2x-1
2x+2=2-10y

3y+2x=-1-6
2x+10y=2-2

2x+3y=-7
2x+10y=0 /:2

2x+3y=-7
x+5y=0

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

2(-5y)+3y=-7
x=-5y

-10y+3y=-7
x=-5y

-7y=-7 /:(-7)
x=-5y

y=1
x=-5

c)
-2(x+2)+3y=-y-4
5(x-1)=x-3(x+y)-1

-2x-4+3y=-y-4
5x-5=x-3x-3y-1

-2x+3y+y=-4+4
5x-x+3x+3y=-1+5

-2x+4y=0 /:(-2)
7x+3y=4

x-2y=0
7x+3y=4

x=2y
7×2y+3y=4

x=2y
14y+3y=4

x=2y
17y=4 /17

x=2y
y=4¼

x=2×4¼
y=4¼

x=8½
y=4¼

d)
2(x-4y)+4x-y=0
4x-4y=-8 /:4

2x-8y+4x-y=0
x-y=-2

2x+4x-8y-y=0
x=-2+y

6x-9y=0
x=-2+y

6(-2+y)-9y=0
x=-2+y

-12+6y-9y=0
x=-2+y

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

y=-4
x=-6





3 4 3
Najlepsza Odpowiedź!
2010-03-12T17:53:32+01:00
A)
{x-3(y-3x)=3x-4
{2(2x-y)=4

{x-3y+9x=3x-4
{4x-2y=4 /:(-2)

{x + 9x - 3x - 3y = -4
{-2x + y = -2

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

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

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

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

{x = -10
{y = -2 + 2×(-10)

{x = -10
{y = -22

b)
{3(2+y) = -2x -1
{2(x+1) = 2 -10y

{6 + 3y = -2x - 1
{2x + 2 = 2 - 10y

{3y + 2x = -1 -6
{2x + 10y =2 -2

{2x + 3y = -7
{2x + 10y = 0 /:2

{2x + 3y= -7
{x + 5y = 0

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

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

{-10y + 3y = -7
{x = -5y

{-7y = -7 /:(-7)
{x = -5y

{y = 1
{x = -5

c)
{-2(x+2) + 3y = -y -4
{5(x-1)= x - 3(x+y) - 1

{-2x - 4 + 3y = -y - 4
{5x - 5 = x - 3x - 3y - 1

{-2x + 3y + y = -4 + 4
{5x - x + 3x + 3y = -1 + 5

{-2x + 4y = 0 /:(-2)
{7x+3y = 4

{x - 2y = 0
{7x + 3y = 4

{x = 2y
{7× 2y + 3y = 4

{x = 2y
{14y + 3y = 4

{x = 2y
{17y = 4 /:17

{x= 2y
{y= 4¼

{x= 2 × 4¼
{y= 4¼

{x= 8½
{y= 4¼

d)
{2(x-4y) + 4x - y = 0
{4x - 4y = -8 /:4

{2x - 8y + 4x -y = 0
{x - y = -2

{2x + 4x - 8y - y = 0
{x = -2 + y

{6x - 9y = 0
{x = -2 + y

{6(-2+y) - 9y = 0
{x = -2 + y

{-12 + 6y - 9y = 0
{x = -2 + y

{-3y = 12 /:(-3)
{x = -2 + y

{y = -4
{x = -6
23 4 23