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2010-01-09T11:34:55+01:00
{ x/4 + y/4 = 2
x/6 - 2 = -y/3
x + y = 8 - mnożymy przez - 1
x - 12 = - 2
-x - y = -8
x - 12 = -2
dodajemy
-y - 12 = - 10
-y = -10 + 12
-y = 2
y = -2
x + y = 8
x - 2 = 8
x = 8 + 2 = 10
x = 10
y = -2
x + y = 8
x - 2 = 8
x = 8 + 2
x = 10
odp x = 10 , y = -2
zad 2
{ x+y/2 - 2y/3 = 5/2
3x/2 + 2y = 0
3x + 6 - 4y = 15
3x + 4y = 0
3x - 4y = 9
3x + 4y = 0
dodajemy
6x = 9
x = 9/6 = 3/2
3x + 4y = 0
9/2 + 4y = 0
4y = 9/2
y = 9/8
odp
x = 3/2
y = 9/8
2010-01-09T11:40:02+01:00
A) { x/4 + y/4 = 2 |*4
x/6 - 2 = -y/3 |*6

x+y=8
x-12=2y |*(-1)

x+y=8
-x+12=-2y

x+y=8
-x+2y=-12
_________________________________

x+y-x+2y=8-12

3y=-4 |:3
y=4/3
y=1 i 1/3

x+y=8
x=8-y
x=8-1 i 1/3
x=6 i 2/3

{y=1i1/3
x=6i 2/3

b) { x+y/2 - 2y/3 = 5/2 |*6
3x/2 + 2y = 0 |*(-4)

6x+3y-4y=15
-6x-8y=0

6x-y=15
-6x-8y=0
__________________________________
6x-y-6x-8y=15

9y=15 |:9
y=15/9
y=1i 2/3

6x-y=15
6x=15+y
6x=15+1i 2/3
6x=16i 2/3 |:6
16i 2/3
x= _________
6

{y=1i 2/3
16i 2/3
x= _________
6