P I L N E ! ! ! Przykłady w załączniku proszę o rozwiązanie tylko zad 1.
1.
{2x+y=4
{x-y=5
---------- +
3x=9
x=3
3-y=5
-y=2
y=-2
{x=3
{y=-2
----------------------------------------------------------------------------------------------------
{x+y=6
{-x-y=0
0≠6 --> równanie sprzeczne
{x+y=4 /·(-3)
{3x+3y=12
{-3x-3y=-12
0=0 --> równanie tożsamościowe
{⅓x+2y=8
{⅔x-2y=3
x=11
⅓·11+2y=8
3⅔+2y=8
2y=4⅓
y=2⅙
{x=11
{y=2⅙
{-3x-y=-9
{3x+2y=9
y=0
3x+0=9
{y=0
{(7x-3y)/5=(7x-5y)/6 /·30
{3x-5y=8
{42x-18y=35x-25y
{3x-5y=8 /·⁷/₅
{7x+7y=0
{4⅕x-7y=11⅕
11⅕x=11⅕
x=1
7+7y=0
7y=-7
y=-1
{x=1
{y=-1
{3x+2y=11
{x²-4+2y=(x-2)²+y
{x²-4+2y=x²+4-4x+y
{-4+2y=4-4x+y
{4x+y=8 /·(-2)
{-8x-2y=-16
-5x=-5
3+2y=11
2y=8
y=4
{y=4
{-2,5x-2y=9 /·2
{5x+4y=11
{-5x-4y=18
0≠29 --> równanie sprzeczne
{-3x+3y=-6 /·2
{6x-6y=12
{-6x+6y=-12
{7x-13=12y-20
{x+3y=8x-8y
{7x-12y=-7
{-7x+11y=0
-y=-7
y=7
x+3·7=8x-8·7
x+21=8x-56
-7x=-77
{y=7
2.
x --> jedna liczba
y --> druga liczba
{x+y=56
{x:y=3:4 /·y
{x=¾y
{¾y+y=56
{1¾y=56 /:1¾
{y=32
{x=¾·32
{x=24
Są to liczby 24 i 32.
3.
x --> obecny wiek Zosi
y --> obecny wiek Marysi
{x+5+y+5=36
{x+4=y
{x+y=26
{y=x+4
{x+x+4=26
{2x=22
{y=11+4
{y=15
Zosia ma 11 lat, a Marysia 15 lat.
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1.
{2x+y=4
{x-y=5
---------- +
3x=9
x=3
3-y=5
-y=2
y=-2
{x=3
{y=-2
----------------------------------------------------------------------------------------------------
{x+y=6
{-x-y=0
---------- +
0≠6 --> równanie sprzeczne
----------------------------------------------------------------------------------------------------
{x+y=4 /·(-3)
{3x+3y=12
{-3x-3y=-12
{3x+3y=12
---------- +
0=0 --> równanie tożsamościowe
----------------------------------------------------------------------------------------------------
{⅓x+2y=8
{⅔x-2y=3
---------- +
x=11
⅓·11+2y=8
3⅔+2y=8
2y=4⅓
y=2⅙
{x=11
{y=2⅙
----------------------------------------------------------------------------------------------------
{-3x-y=-9
{3x+2y=9
---------- +
y=0
3x+0=9
3x=9
x=3
{x=3
{y=0
----------------------------------------------------------------------------------------------------
{(7x-3y)/5=(7x-5y)/6 /·30
{3x-5y=8
{42x-18y=35x-25y
{3x-5y=8 /·⁷/₅
{7x+7y=0
{4⅕x-7y=11⅕
---------- +
11⅕x=11⅕
x=1
7+7y=0
7y=-7
y=-1
{x=1
{y=-1
----------------------------------------------------------------------------------------------------
{3x+2y=11
{x²-4+2y=(x-2)²+y
{3x+2y=11
{x²-4+2y=x²+4-4x+y
{3x+2y=11
{-4+2y=4-4x+y
{3x+2y=11
{4x+y=8 /·(-2)
{3x+2y=11
{-8x-2y=-16
---------- +
-5x=-5
x=1
3+2y=11
2y=8
y=4
{x=1
{y=4
----------------------------------------------------------------------------------------------------
{-2,5x-2y=9 /·2
{5x+4y=11
{-5x-4y=18
{5x+4y=11
---------- +
0≠29 --> równanie sprzeczne
----------------------------------------------------------------------------------------------------
{-3x+3y=-6 /·2
{6x-6y=12
{-6x+6y=-12
{6x-6y=12
---------- +
0=0 --> równanie tożsamościowe
----------------------------------------------------------------------------------------------------
{7x-13=12y-20
{x+3y=8x-8y
{7x-12y=-7
{-7x+11y=0
---------- +
-y=-7
y=7
x+3·7=8x-8·7
x+21=8x-56
-7x=-77
x=11
{x=11
{y=7
2.
x --> jedna liczba
y --> druga liczba
{x+y=56
{x:y=3:4 /·y
{x+y=56
{x=¾y
{¾y+y=56
{x=¾y
{1¾y=56 /:1¾
{x=¾y
{y=32
{x=¾y
{y=32
{x=¾·32
{y=32
{x=24
Są to liczby 24 i 32.
3.
x --> obecny wiek Zosi
y --> obecny wiek Marysi
{x+5+y+5=36
{x+4=y
{x+y=26
{y=x+4
{x+x+4=26
{y=x+4
{2x=22
{y=x+4
{x=11
{y=x+4
{x=11
{y=11+4
{x=11
{y=15
Zosia ma 11 lat, a Marysia 15 lat.