Rozwiąż układy równań metodą postawiania :

a) x + 3y = 3
x - y = 5

b) 2x - y = 10
x + 5y = -17

c) 3m + n = 9
2m - 5n = -11

d) ½x - 2y = 8
2x + 5y = 6

e) ½x - ¾y = 0
⅔x + 1¼y = 9

f) 3x + 4y = 1⅔
6x + 3y = 1¼

! PROSZE W MIARĘ ZROZUMIALE :P ! DZIĘKUJE . :D !

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Odpowiedzi

2010-01-11T18:20:06+01:00
A) x + 3y = 3
x - y = 5

x=3-3y
3-3y-y=5

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

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

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

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

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

x=3+1i1/2
y=-1/2

x=4i1/2
y=-1/2

b) 2x - y = 10
x + 5y = -17

2x-y=10
x=-17-5y

2*(-17-5y)-y=10
x=-17-5y

-34-10y-y=10
x=-17-5y

-11y=10+34
x=-17-5y

-11y=44/:(-11)
x=-17-5y

y=-4
x=-17-5*(-4)

y=-4
x=3

c) 3m + n = 9
2m - 5n = -11

n=9-3m
2m-5*(9-3m)=-11

n=9-3m
2m-45+15m=-11

n=9-3m
17m=-11+45

n=9-3m
17m=34/17

n=9-3m
m=2

n=9-3*2
m=2

n=3
m=2

d) ½x - 2y = 8
2x + 5y = 6

1/2x=8+2y/*2
2x+5y=6

x=16+4y
2*(16+4y)+5y=6

x=16+4y
32+8y+5y=6

x=16+4y
13y=6-32

x=16+4y
13y=-26/:13

x=16+4y
y=-2

x=16+4*(-2)
y=-2

x=16-8
y=-2

x=8
y=-2

e) ½x - ¾y = 0
⅔x + 1¼y = 9

1/2x=3/4y/*2
2/3x+1i1/4y=9

x=3/2y
2/3*3/2y+1i1/4y=9

x=3/2y
y+1i1/4y=9

x=3/2y
2i1/4y=9/:2i1/4

x=3/2y
y=4

x=3/2*4
y=4

x=6
y=4

f) 3x + 4y = 1⅔
6x + 3y = 1¼

4y=1i2/3-3x/:4
6x + 3y = 1¼

y=5/12-3/4x
6x+3(5/12-3/4x)=1i1/4

y=5/12-3/4x
6x+5/4-9/4x=1i1/4

y=5/12-3/4x
3i3/4x=1i1/4-5/4

y=5/12-3/4x
3i3/4x=0/:3i3/4

y=5/12-3/4x
x=0

y=5/12-3/4*0
x=0

y=5/12
x=0
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