1.Rozwiąż układy równań metodą podstawiania.PROSZĘ POMÓC.
a){x+3y=3
{x-y=5
b){2x-y=10
{x+5y=-17
c){3m+n=9
{2m-5n=-11
d){4a-2=b
{3a+7b=1,5
e){5x=4-2y
{4x+y=3
f){6x-3y=9
{x+5y=9,5
2.Rozwiąż podobne układy równań metodą podstawiania.
a){x+2y=-2
{2x-y=1
b){x+4y=-2
{3x-8y=10
c){x-2y=3
{-2x+y=0
d){2x+y=9
{5x-4y=3
e){3x-2y=5
{2x-y=4
f){2x+9y=-9
{-3x+3y=8
g){2x+3y=4
{8x-5y=-1
h){x-y=0
{x+y+z=4
{x+2y+3z=9

3

Odpowiedzi

2010-01-30T15:18:47+01:00
Zad1.

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

x+3y=3
x=5-y

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

5+2y=3
x=5-y

2y=3-5
x=5-y

2y=-2/:2
x=5-y

y=-1
x=5+1

y=-1
x=6

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

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

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

-34-6y=10
x=-17-5y

-6y=10+34
x=-17-5y

-6y=44/:(-6)
x=-17-5y

y=-7,3
x=-17-5y

y=-7,3
x=-17-5(-7,3)

y=-7,3
x=-17+12,3

y=-7,3
x=-4,7

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

n=9-3m
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=9+6
m=-2

n=15
m=-2


d)
4a-2=b
3a+7b=1,5

b=4a-2
3a+7(4a-2)=1,5

b=4a-2
3a+28a-14=1,5

b=4a-2
31a=1,5+14

b=4a-2
31a=15,5/:31

b=4a-2
a=0,5

b=4(0,5)-2
a=0,5

b=2-2
a=0,5

a=0,5
b=0

e)
5x=4-2y
4x+y=3

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

5x=4-2(3-4x)
y=3-4x

5x=4-6+16x
y=3-4x

5x-16x=-2
y=3-4x

-11x=-2/:(-11)
y=3-4x

x=0,18
y=3-4(0,18)

x=0,18
y=3-0,72

x=0,18
y=2,28

f)
6x-3y=9
x+5y=9,5

6x-3y=9
x=9,5-5y

6(9,5-5y)-3y=9
x=9,5-5y

57-30y-3y=9
x=9,5-5y

33y=9-57
x=9,5-5y

33y=-45/:33
x=9,5-5y

y=-1,36
x=9,5-5y

y=-1,36
x=9,5-5(-1,36)

x=9,5+6,8
y=-1,36

x=16,3
y=-1,36








2010-01-30T15:23:56+01:00
A){x+3y=3
{x-y=5
{x+3y=3
{x=5+y
{5+y+3y=3
{x=5+y
{4y=3-5
{x=5+y
{4y=-2 /:4
{x=5+y
{y=-2/4
{x=5+y
{y=-½
{x=5+(-½)
{y=-½
{x=5/1-1/2
{y=-½
{x=10/2-1/2
{y=-½
{x=9/2

spr.
x-y=5
9/2-(-½)=5
9/2+1/2=5
10/2=5
5=5

b){2x-y=10
{x+5y=-17
{-y=10-2x /×(-1)
{x+5y=-17
{y=-10+2x
{x+5y=-17
{y=-10+2x
{x+5×(-10+2x)=-17
{y=-10+2x
{x-50+10x=-17
{y=-10+2x
{11x=-17+50
{y=-10+2x
{11x=33 /:11
{y=-10+2x
{x=3
{y=-10+2×3
{x=3
{y=-10+6
{x=3
[y=-4
{x=3

spr.
x+5y=-17
3+5×(-4)=-17
3-20=-17
-17=-17

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=9-6
{m=2
{n=3
{m=2

spr.
3m+n=9
3×2+3=9
6+3=9
9=9

d){4a-2=b
{3a+7b=1,5
{b=4a-2
{3a+7×(4a-2)=1,5
{b=4a-2
{3a+28a-14=1,5
{b=4a-2
{31a=1,5+14
{b=4a-2
{31a=15,5 /:31
{b=4a-2
{a=1/2
{b=4×1/2-2
{a=1/2
{b=2-2
{a=1/2
{b=0
{a=1/2

spr.
3a=7b=1,5
3×1/2+7×0=1,5
1,5=1,5


  • Fao
  • Rozwiązujący
2010-01-30T15:24:52+01:00
1.
a){x+3y=3 / -3y
{x-y=5

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

x=3-3y
-4y=2

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

x= 3-3 × (-1/2)
y=-1/2

x=4,5
y=-0,5

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

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

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

y=2x-10
x+10x-50=-17

y=2x-10
11x=33

x=11
y=22-10

x=11
y=12

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

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

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

n=9-3m
17m = 34

m=2
n=3

d){4a-2=b
{3a+7b=1,5

b=4a-2
3a+7(4a-2)=1,5

b=4a-2
3a+28a-14 = 1,5

b=4a-2
31a = 15,5

a=0,5
b=0

e){5x=4-2y
{4x+y=3 / -4x

y=3-4x
5x=4-2(3-4x)

y=3-4x
5x=4-6=4x

x=-2
y=3-4×(-2)

x=-2
y= 11

f){6x-3y=9
{x+5y=9,5

x=9,5-5y
6×(9,5-5y) - 3y =9

x=9,5n- 5y
57 - 30y - 3y =9

x=9,5 - 5y
-33y = -48

x=9,5 - 5u
y = 16/11

x=9,5 -5× 16/11
y=16/11

x=2,(23)
y=1,(45)

2.

a){x+2y=-2 /-2y
{2x-y=1

x=-2-2y
2×(-2-2y) - y =1

x=-2-2y
-4-4y-y = 1

x=-2-2y
-5y = 5

x=-2-2y
y=-1

x=-2-2×(-1)
y=-1

x=0
y=-1

b){x+4y=-2 / -4y
{3x-8y=10

x=-2-4y
3×(-2-4y) - 8y = 10

x=-2-4y
-6-12y-8y =10

x=-2-4y
-20y = 16

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

x= -2 -4×(-0,8)
y=-0,8

x=1,2
y=-0,8

c){x-2y=3 /+2y
{-2x+y=0

x=3+2y
-2(3+2y) +y=0

x=3+2y
-6-4y+y=0

x=3+2y
-3y=6

x=3+2y
y=-2

x=-1
y=-2


d){2x+y=9 /-2x
{5x-4y=3

y=9-2x
5x-4(9-2x) = 3

y=9-2x
5x-36+8x = 3

13x=39
y=9-2x

x=3
y=3

e){3x-2y=5
{2x-y=4 /-2x

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

3x-2(2x-4) = 5
y=2x-4

3x-4x+8= 5
y=2x-4

-x = -3
y=2×3-4

x=3
y=2

f){2x+9y=-9 /-9y
{-3x+3y=8

2x=-9 -9y
-3x+3y=8

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

x=-4,5-4,5y
-3(-4,5-4,5y) +3y =8

x=-4,5-4,5y
13,5 + 16,5y =8

x=-4,5 -4,5y
16,5y= 5,5

x=-4,5-4,5y
y = 1/3

x=-4,5 -4,5 × 1/3
y=1/3

x=6
y=1/3

g){2x+3y=4
{8x-5y=-1

x=(4-3y)/2
8×(4-3y/2) - 5y =-1

x=(4-3y)/2
16 - 12y -5y = -1

x=(4-3y)/2
-17y =-17

x=(4-3y)/2
y=1

x= 1/2
y=1

h){x-y=0 /+y
{x+y+z=4
{x+2y+3z=9

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

x=y
z=4-2y
3y+3(4-2y) =9

x=y
z=4-2y
3y+12-6y=9

x=y
z=4-2y
-3y=-3

x=y
y=1
z=2

x=1
y=1
z=2