Zad 11 str 112 Matematyka Z Plusem Druga gimnazjum.

Rozwiąż układy równań.
/ - kreska ułamkowa

a) 3(x-½) + 2(y+3) = 3½
3x-1 /3 - y + 3 /2 = -1

b) x-3 /4 - y+5 /2 = -1,5
x-3 /2 - 2y-7 /3 = 1

c) 2x-5 /2 - x-6y /4 = x+y /2
3x-1 /10 + 2y-5 /5 = 2x +y /2

d) x-3 /5 - y + 1 /2 = 1 - (x-y)
4x -1 /3 - y-3 /6 = 2 (x-y)

Wychodzi mi kompletnie co innego, niż powinno. ;( Pomocy !

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Odpowiedzi

Najlepsza Odpowiedź!
2010-02-09T12:07:24+01:00
A) 3(x-½) + 2(y+3) = 3½
3x-1 /3 - y + 3 /2 = -1(*6)

3x-3/2+2y+6=3i1/2 (*2)
2(3x)-2(3/2)+2(2y)+2(6)=2(7/2)
6(3x)-6(1/3)-6y+6(3/2)=6(-1)

6x-3+4y+12=7
18x-2-6y+9=-6

4y=7-12+3-6x
18x=-6-9+2+6y

4y=-2-6x
y=-1/2-3/2x
18x=-13+6(-1/2-3/2x)

y=-1/2-3/2x
18x=-13-3-9x

y=-1/2-3/2x
18x+9x=-16
27x=-16
x=-16/27
y=-1/2-3/2(-16/27)
y=-1/2+24/27
y=-1/2+8/9
y=-9/18+16/18
y=7/18
x=-16/27



b) x-3 /4 - y+5 /2 = -1,5
x-3 /2 - 2y-7 /3 = 1
x-3/4-y+5/2=-1i1/2 (*4)
x-3/2-2y-7/3=1(*6)

4x-4(3/4)-4y+4(5/2)=4(-3/2)
6x-6(3/2)-6(2y)-6(7/3)=6
4x-3-4y+10=-6
6x-9-12y-14=6

4x=-6-10+3+4y
4x=-13+4y
x=-13/4+y
6(y-13/4)-23-12y=6
6y-39/2-23-12y=6
-6y=6+23+39/2
-6y=48i1/2
y=19/2*(-1/6)
y=-19/12
x=-13/4-19/12
x=-3i1/4-1i7/12
x=-3i3/12-1i7/12
x=-4i10/12
x=-4i5/6
y=-19/12
y=-1i7/12


c) 2x-5 /2 - x-6y /4 = x+y /2(*4)
3x-1 /10 + 2y-5 /5 = 2x +y /2 (*10)

4(2x)-4(5/2)-4x-4(6y/4)=4x+4y
8x-10-4x-6y=4x+4y
-6y-4y=4x-8x+4x+10
-10y=10
y=-1
10(3x)-10(1/10)+10(2y)-10(5/5)=10(2x)+10(y/2)
30x-1+20y-10=20x+5y
30x-20x=5y-20y+11
10x=-15y+11
x=-1,5+1,1
x=-0,4
y=-1


d) x-3 /5 - y + 1 /2 = 1 - (x-y)
4x -1 /3 - y-3 /6 = 2 (x-y)
x-3/5-y+1/2=1-x+y(*10)
4x-1/3-y-3/6=2x-2y(*6)

10x-10(3/5)-10y+10(1/2)=10-10x+10y
10x-6-10y+5=10-10x+10y
10x+10x=10+10y+10y+6-5
20x=20y+11
x=y+11/20

6(4x)-6(1/3)-6y-6(3/6)=6(2x)-6(2y)
24x-2-6y-3=12x-12y
-6y+12y=12x-24x+5
6y=5-12x
y=5/6-2x

y=5/6-2(y+11/20)
y=5/6-2y-11/10
y+2y=5/6-11/10
3y=25/30-33/30
3y=-8/30
y=-8/30*1/3
y=-8/90
x=-8/90+11/20
x=-16/180+99/180
x=83/180
y=-8/90
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