Temat do zadania: Rozwiązywanie układów równań

Zadanie: Rozwiąż układy równań metodą podstawiania
/ - to będzie zastępować klamrę
\
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

3

Odpowiedzi

2010-01-25T09:54:50+01:00
A)

x + 3y = 3 / * (-1)
x - y = 5

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

-4y = 2 / : (-4)
y = 0,5

y = 0,5
x - 0,5 = 5

y = 0,5
x = 5 + 0,5

y = 0,5
x = 5,5

b)

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

2x - y = 10
- 2x - 10y = 34

-11y = 44 / : (-11)
y = -4

y = -4
2x - 4 = 10

y = -4
2x = 10-4

y = -4
2x = 6

y = -4
x = 3


c )


3m + n = 9 / * 5
2m - 5n = -11

15m + 5n = 45
2m - 5n = -11

17m = 34/ : 17
m = 2

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

m = 2
4 - 5n = -11

m = 2
-5n = -11-4

m = 2
-5n = -15 / :(-5)

m = 2
n = 3


d)

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

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

-28a - 7b = -14
3a + 7b = 1,5

-25a = -12,5 / : (-25)
a = 0,5

a = 0,5
(4*0,5) + b = 2

a = 0,5
2 + b = 2

a = 0,5
b = 2-2

a= 0,5
b = 0

2010-01-25T11:55:29+01:00
/ x+3y =3
\ x-y =5 / * 3

/ x +3y=3
\ 3x-3y =15
4x=18 /:4
x=4.5
/ x=4.5
\ 4.5+3y=3

/ x=4.5
\ 3y=3-4.5

/ x=4.5
\ 3y=-1.5/:3

/ x=4.5
\ y=-0.5

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

/ 10x-5y=50
\ x+5y=-17
11x = 33 / : 11
x=3

/ x=3
\ 2*3-y=10

/ x=3
\ 6-y=10

/ x=3
\ -y=10-6

/x=3
\ -y = 4 / * -1

/x=3
\ y = -4

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

/ 15m+5n=45
\ 2m-5n=-11
17m = 34 / : 17
m=2

/ m=2
\ 3*2+n=9

/ m=2
\ 6+n=9

/ m=2
\ n= 9-6

/ m=2
\ n=3

/ 4a - 2 = b
\ 3a + 7b = 1,5

/ 4a-b=2/*-7
\ 3a-7b=1.5

-28a+7b = -14
3a-7b=1.5
-25a= -12.5/:-25
a=0.5

/a=0.5
\ 4*0.5-b=2

/a=0.5
\ 2-b=2

/a=0.5
\ -b=2-2

/a=0.5
\ -b=0 \* -1

/a=.5
\ b= 0

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

/ 5x+2y=4/*-1
\ 5x+y=3
-5x-2y=-4
5x+y =3
y=1

/y=1
\ 5x+2*1=4

/y=1
\5x+2=4

/y=1
\ 5x=4+6

/ y=1
\ 5x=10 /: 5

/ y=1
\x=2



f)
/ 6x - 3y = 9 / *1
\ x + 5y = -9,5 / * -6

/ 6x-3y=9
\ -6-30y = 57
-33y = 66 / : -33
y=-2

/y=-2
\ 6x-3*-2=9

/y=-2
\ 6x +6=9

/y =-2
\ 6x=9-6

/y=-2
\6x=3 /:6

/ y=-2
\ x=0.5


2010-01-25T13:30:08+01:00
A)
/ x+3y =3
\ x-y =5


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


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


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


x=3-3y
y=½


x=3-3*½
y=½


x=3-1½
y=½


x=1½
y=½



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=-17+20


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 = 9-6
m = 2


n = 3
m = 2


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


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


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


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


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


4a - 2 = b
a = 0,5


4*0,5 -2 = b
a = 0,5


2-2=b
a = 0,5

b = 0
a = 0,5


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


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


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


5x = 4 - 6 + 8x
y = 3-4x


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


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


x= ²/₃ (dwie trzecie)
y = 3 - 4 * ²/₃ (dwie trzecie)


x = ²/₃
y = 3 - 2²/₃


x = ²/₃
y = 1²/₃

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 = 66 /:(-33)
x = -9,5 - 5y


y = -2
x = -9,5 - 5*(-2)


y = -2
x = -9,5 + 10


y = -2
x = ½


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