Prosze o rozwiazanie
zadanie w zalaczniku
zadanie numer 10 rozwiazcie metoda przeciwnych wspolczynnikow
zad.10
a)
x/2 + y/3 = 1 1/3 / *6
x/3 - y/2 = 2 1/3 / *6
3x +2y = 8 / *2
2x - 3y = 14 / * (-3)
6x + 4y = 16
-6x + 9y = - 42 +
------------------------
13y = -26 / : 13
y= - 2
3x + 2y = 8
3x + 2 * (-2) = 8
3x = 8 + 4
3x = 12 / : 3
x= 4
y= -2
b)
3/5x + 1/2y = 2 /*10
1/2 (2x-y) =2
6x+5y = 20
x- 1/2y = 2 / * (-6)
-6x +3y = -12 +
---------------------
8y = 8 / : 8
y=1
6x+5*1=20
6x=15/:6
x= 15/6
x=2,5
c)(x+2)/5-2y=5 |*5x-(y+2)/6=3 |*6x+2-10y=256x-y-2=18x-10y=236x-y=20x=23+10y6(23+10y)-y=20x=23+10y138+60y-y=20x=23+10y59y=-118 |:59x=23+10yy=-2x=23+(-2*10)=23-20=3d)(x+y)/2-x/3=4 |*6(x-y)/2+y/3=-3 |*63x+3y-2x=243x-3y+2y=-18x+3y=243x-y=-18x=24-3y3(24-3y)-y=-18x=24-3y72-9y=-18x=24-3y9y=90 |:9x=24-3yy=10x=24-30=-6e)(3x-1)/5+(2y-3)/4=(3y+3)/2 |*20(x+y)/4-(3y-1)/2=(x-6y)/4 *412x-4+10y-15=30y+30x+y-(6y-2)=x-6y12x+10y-19=30y+30x+y-6y+2=x-6y12x+10y-30y=49x-5y-x+6y=-212x-20y=49y=-212x=49+20yy=-212x=49-40=9x=0,75f)(3x-2)/3-(2x+y)/6=x+1/6 |*6x+y-(-x+y)/5=1/5-0,8x |*56x-4-2x-y=6x+15x+5y+x-y=1-4x4x-4-y=6x+16x+4y=1-4x-2x-y=510x+4y=1y=-2x-510x+4(-2x-5)=1y=-2x-510x-8x-20=1y=-2x-52x=21 |:2y=-2x-5x=10,5y=-21-5=-26
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zad.10
a)
x/2 + y/3 = 1 1/3 / *6
x/3 - y/2 = 2 1/3 / *6
3x +2y = 8 / *2
2x - 3y = 14 / * (-3)
6x + 4y = 16
-6x + 9y = - 42 +
------------------------
13y = -26 / : 13
y= - 2
3x + 2y = 8
3x + 2 * (-2) = 8
3x = 8 + 4
3x = 12 / : 3
x= 4
y= -2
b)
3/5x + 1/2y = 2 /*10
1/2 (2x-y) =2
6x+5y = 20
x- 1/2y = 2 / * (-6)
6x+5y = 20
-6x +3y = -12 +
---------------------
8y = 8 / : 8
y=1
6x+5y = 20
6x+5*1=20
6x=15/:6
x= 15/6
x=2,5
y=1
c)
(x+2)/5-2y=5 |*5
x-(y+2)/6=3 |*6
x+2-10y=25
6x-y-2=18
x-10y=23
6x-y=20
x=23+10y
6(23+10y)-y=20
x=23+10y
138+60y-y=20
x=23+10y
59y=-118 |:59
x=23+10y
y=-2
x=23+(-2*10)=23-20=3
d)
(x+y)/2-x/3=4 |*6
(x-y)/2+y/3=-3 |*6
3x+3y-2x=24
3x-3y+2y=-18
x+3y=24
3x-y=-18
x=24-3y
3(24-3y)-y=-18
x=24-3y
72-9y=-18
x=24-3y
9y=90 |:9
x=24-3y
y=10
x=24-30=-6
e)
(3x-1)/5+(2y-3)/4=(3y+3)/2 |*20
(x+y)/4-(3y-1)/2=(x-6y)/4 *4
12x-4+10y-15=30y+30
x+y-(6y-2)=x-6y
12x+10y-19=30y+30
x+y-6y+2=x-6y
12x+10y-30y=49
x-5y-x+6y=-2
12x-20y=49
y=-2
12x=49+20y
y=-2
12x=49-40=9
x=0,75
f)
(3x-2)/3-(2x+y)/6=x+1/6 |*6
x+y-(-x+y)/5=1/5-0,8x |*5
6x-4-2x-y=6x+1
5x+5y+x-y=1-4x
4x-4-y=6x+1
6x+4y=1-4x
-2x-y=5
10x+4y=1
y=-2x-5
10x+4(-2x-5)=1
y=-2x-5
10x-8x-20=1
y=-2x-5
2x=21 |:2
y=-2x-5
x=10,5
y=-21-5=-26