rozwiaz uklad rownan. trzeba obliczyc x i y :)
DAJE NAJ:*
a)x+y=5x-2y=-1y=5-xx-2(5-x) = -1y=5-xx-10+2x=-1y=5-x3x = 9 /:3y=5-xx = 3y=5-3x=3y=2x=3
b)y-x=43(x+y)=24y-x=43x+3y=24y=4+x3x+3(4+x)=24y=4+x3x+12+3x=24y=4+x6x = 12 /:6y=4+xx=2y=4+2x=2y=6x=2c)x-2y=4x+3=2yx-2y=4x-2y=-3x=4+2y4+2y-2y=-3x=4+2y2y-2y=-7x=4+2y0=-7 układ równań sprzeczny.d)3x-1=y-24x-3=-2(y-2)3x-y=-14x-3=-2y+43x-y=-14x+2y=7-y=-1-3x /:(-1)4x+2y=7y=1+3x4x+2(1+3x)=7y=1+3x4x+2+6x=7y=1+3x10x = 5 /:10y=1+3xx=0,5y=1+3*0,5x=0,5y=2,5x=0,5e)0,5(x-1)+y=-2,5x-7=1-y0,5x-0,5+y=-2,5x+y=80,5x+y=-2x=8-y0,5(8-y)+y=-2x=8-y4-0,5y+y=-2x=8-y0,5y= -6 /:0,5x=8-yy= -12x=8-(-12)y=-12x=20
f)x-y x+y 1--- - --- = - --- /*6 3 2 2
x+y=32(x-y)-3(x+y)=-3x+y=32x-2y-3x-3y=-3x+y=3-x-5y=-3x=3-y-(3-y)-5y=-3x=3-y-3+y-5y=-3x=3-y-4y = 0 /:(-4)x=3-yy=0x=3-0y=0x=3
a)
b)
c)
brak rozwiązania
d)
e)
f)
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a)
x+y=5
x-2y=-1
y=5-x
x-2(5-x) = -1
y=5-x
x-10+2x=-1
y=5-x
3x = 9 /:3
y=5-x
x = 3
y=5-3
x=3
y=2
x=3
b)
y-x=4
3(x+y)=24
y-x=4
3x+3y=24
y=4+x
3x+3(4+x)=24
y=4+x
3x+12+3x=24
y=4+x
6x = 12 /:6
y=4+x
x=2
y=4+2
x=2
y=6
x=2
c)
x-2y=4
x+3=2y
x-2y=4
x-2y=-3
x=4+2y
4+2y-2y=-3
x=4+2y
2y-2y=-7
x=4+2y
0=-7 układ równań sprzeczny.
d)
3x-1=y-2
4x-3=-2(y-2)
3x-y=-1
4x-3=-2y+4
3x-y=-1
4x+2y=7
-y=-1-3x /:(-1)
4x+2y=7
y=1+3x
4x+2(1+3x)=7
y=1+3x
4x+2+6x=7
y=1+3x
10x = 5 /:10
y=1+3x
x=0,5
y=1+3*0,5
x=0,5
y=2,5
x=0,5
e)
0,5(x-1)+y=-2,5
x-7=1-y
0,5x-0,5+y=-2,5
x+y=8
0,5x+y=-2
x=8-y
0,5(8-y)+y=-2
x=8-y
4-0,5y+y=-2
x=8-y
0,5y= -6 /:0,5
x=8-y
y= -12
x=8-(-12)
y=-12
x=20
f)
x-y x+y 1
--- - --- = - --- /*6
3 2 2
x+y=3
2(x-y)-3(x+y)=-3
x+y=3
2x-2y-3x-3y=-3
x+y=3
-x-5y=-3
x=3-y
-(3-y)-5y=-3
x=3-y
-3+y-5y=-3
x=3-y
-4y = 0 /:(-4)
x=3-y
y=0
x=3-0
y=0
x=3
a)
b)
c)
brak rozwiązania
d)
e)
f)
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