Odpowiedzi

2010-03-28T14:09:45+02:00
1. (a)
2(x-1)+3(y-2)=5
3(x+y)-2(x+2)=7

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

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

2x+3y=13
x+3y=11/: (-1)

2x+3y=13
-x-3y=-11
x=2

x=2
2+3y=11

x=2
y=3
2. (b)
3(x-1)+2(2-y)=-5-y
x+y=2
3x-3+4-2y=-5-y
x+y=2
3x-2y+y=-5+3-4
x+y=2
3x-y=-6
x+y=2
4x=-4/:4
x=-1
x=-1
-1+y=2
x=-1
y=3
3. (c)
2(x+3)-3(x+y)=8
5x-3y=1
2x+6-3x-3y=8
5x-3y=1
-x-3y=8-6
5x-3y=1
-x-3y=2
5x-3y=1/:-1
-x-3y=2
-5x+3y=-1
-6x=-1/:(-6)
x=1/6
2*1/6+6-3*1/6-3y=8
x=1/6
-3y=8+2/6-6
x=1/6
x=1/6
y=7/9
4. (d)
y/4+ 2x-14/8=x-1/2 /:8
3x+y=2+x
2y+2x-14=4(x-1)
3x+y-x=2
2y+2x-14=4x-4
2x+y=2
2y+2x-4x=-4+14
2x+y=2
2y-2x=10
y+2x=2
3y=12/:3
y=4
2x+4=2
y=4
2x=2-4
y=4
x=-1
y=4
5. (e)
2x+4/2+y+1/3=4 /* 6
3(x+2)-2(y-2)=3x+12
3(2x+4)+2(y+1)=24
3x+6-2y+4=3x+12
6x+2y=24-12-2
0x-2y=2
6x+2y=10
0x-2y=2
6x=12/:6
x=2
6*2+2y=10
x=2
2y=10-12
x=2
2y=-2/:2
y=-1
x=2
6. (f)
x-2/3-y-1/5=-1/3 /*15
x-y=0
5(x-2)-3(y-1)=-5
x-y=0
5x-3y=-5+10-3
x-y=0 /* (-5)
5x-3y=2
-5x+5y=0
2y=2/:2
y=1
y=1
x-1=0
y=1
x=1
7. (g)
7x-3y/5=5x-y/3-x+y/2 /*30
x-1=y+1
6(7x-3y)=10(5x-y)-15(x+y)
x-1=y+1
42x-18y-50x+10y+15x+15y=0
x-y=2
7x+7y=0
x-y=2 /*7
7x+7y=0
7x-7y=14
14x=14/: 14
x=1
1-y=2
x=1
y=-1
y=1
8. (h)
1-x-2y/3=x-y/2+1/6 /*6
2x-3y=5
6-2(x-2y)=6x-3y+1
2x-3y=5
6-2x+4y=6x-3y+1
2x-3y=5
-2x+4y-6x+3y=1-6
2x-3y=5
-8x+7y=-5
2x-3y=5 /*4
-8x+7y=-5
8x-12y=20
5y=15/:5
y=3
y=3
2x-3*3=5
y=3
2x-9=5
y=3
x=7
9. (i)
równanie sprzeczne wynik y=0 , x=0
10. (j)
x+2/4-3-y/3=-1/4 /*12
x+y=0
3(x+2)-4(3-y)=-3
x+y=0
3x+6-12+4y=-3
x+y=0
3x+4y=-3-6+12
x+y=0 /* (-3)
3x+4y=3
-3x-3y=0
y=3
y=3
x+3=0
x=-3
y=3
mam nadzieję ze dobrze :)
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