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Rozwiązane

Zad.1
Rozwiaz podane uklady rownan dowolna metoda.
"∫" klamra
∫
a) ∫3(x-y)+4x=8
∫3(x-5y)=5-9y
b) ∫3(2x-1)+4(y-2)=9
∫2(5x-1)+3y=5(3x+y)+2
c) ∫2(x+y)-3(x-2y)=-7x-2
∫5(x+1)-2(3-y)=-4(x+y)
Zad.2
Rozwiaz uklady rownan.
"/" kreska ulamkowa
a) ∫⅗x+½y=2
∫½(2x-y)=2
b) ∫x+y/2-x/3=4
∫x-y/2+y/3=-3
Z gory dzieki :)

Odpowiedź :

a) ∫3(x-y)+4x=8
∫3(x-5y)=5-9y

3x-3y+4x=8
3x-15y+9y=5

7x-3y=8|*(-2)
3x-6y=5

-14x+6y=-16
3x-6y=5

-14x+6y+3x-6y=-16+5
-11x=-11
x=1

x=1
3x-6y=5

x=1
3*1-6y=5

x=1
3-6y=5

x=1
-6y=2

y=-1/3
b)
∫3(2x-1)+4(y-2)=9
∫2(5x-1)+3y=5(3x+y)+2

6x-3+4y-8=9
10x-2+3y=15x+5y+2

6x+4y=4
-5x-2y=4 /*2

6x+4y=4
+ -10x-4y=8
-4x=12 /:(-4)
x= (-3)

x=(-3)
6x-3+4y-8=9

x= -3
6*(-3)-3+4y-8=9

x= -3
-18-3+4y-8=9

x= -3
4y=38 /:4

x= -3
y=9,5

c) ∫2(x+y)-3(x-2y)=-7x-2
∫5(x+1)-2(3-y)=-4(x+y)

2x+2y-3x+6y=7x-2
5x+5-6+2y=4x+4y

-8x+ 8y= -2
x-2y=1

-8x+8y= -2
x=1+2y

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

-8+1+2y+8y= -2
x=1+2y

10y= 6 /:10
x=1+2y

y= 0.6
x= 1+2*0.6

y=0.6
x=2.2

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