Question

Rozwiąż równania metodą przeciwnych współczynników: a) x/2+y/3=1 1/3 x/3-y/3=2 1/3 b) 3/5 x+ 1/2 y=2 1/2 (2x-y)=2 c) x/2+y/2-2y=5 x-y/6+2/6=3 d) x/2+y/2-x/3=4 x/2-y/2+y/3=-3 e) 3x/5- 1/5+ 2y/4- 3/4= 3(y+1)/2 x/4+y/4-3y/2+3/4= x/4- 6y/4 f) 3x/3-2/3-2x/6+y/6= x+ 1/6 x+y- -x/5+ y/5= 1/5 - 0,8x Jeśli ktoś ma to jest to zad. 10 ze str. 103 matematyka 2 z plusem

Answer 1

a)

x/2+y/3=1 1/3    /*6

 x/3-y/3=2 1/3   /*6

 

3x+2y = 8   /*1,5

2x-3y= 14

 

4,5x +3y = 12

2x-3y= 14

------------------ 

6,5x = 26   /: 6,5

x = 4

3x+2y = 8

 

x=4

3*4+2y = 8

 

x=4

2y = 8 -12

 

x=4

2y = -4   /:2

 

x= 4

y= -2

 

b)

3/5 x+ 1/2 y=2    /*10

 1/2 (2x-y)=2      /*2

 

6x+5y=20

2x-y= 4      /*(-3)

 

6x+5y=20

-6x+3y= -12

---------------------- 

 8y = -8   /:8

y=1

6x+5y=20

 

y=1

6x+5*1=20

 

y=1

6x=20-5

 

y=1

6x=15    /:6

 

y=1

x=2,5

 

c)

 x+2/5 -2y =5     /*5

x -y+2/6 =3      /*6

 

x+2-10y=25

6x=y-2=18

 

x-10y=23    /*(-6)

6x-y=20

 

-6x+60y =-138

 6x-y = 20

----------------

59y=-118    /:59

 

y = -2

x-10y=23

 

y=-2

x-10*(-2) =23

 

y = -2

x+20=23

 

y=-2

x= 3

 

d)

 x+y/2 -x/3 =4       /*6

 x-y/2+y/3 =-3      /*6

 

3(x+y)-2x = 24

3(x-y)+2y = -18

 

3x+3y-2x =24

3x-3y+2y =-18

 

x+3y = 24

3x-y = -18   /*3

 

x+3y = 24

9x -3y = -54

------------------

10x = -30   /:10

x = -3

x+3y = 24

 

x=-3

-3 +3y = 24

 

x=-3

3y = 24+3

 

x=-3

3y=27   /:3

 

x= -3

y= 9

 

e)

 3x-1/5+2y-3/4=3(y+1)/2      /*20

x+y/4 -3y-1/2=x-6y/4          /*4

 

4(3x-1)+5(2y-3)=30(y+1)

x+y-2(3y-1)=x-6y

 

12x-4+10y-15=30y+30

x+y-6y+2=x-6y

 

 

12x+10y-30y=30+19

x+y-6y-x+6y=-2

 

12x-20y=49

y=-2

 

12x-20*(-2)=49

y=-2

 

12x=49-40

y=-2

 

12x=9    /:12

y=-2

 

x=9/12

y=-2

 

x=3/4

y=-2

 

 

f)

 3x-2/3 -2x+y/6=x+1/6       /*6

x+y- -x+y/5 =1/5-0,8x         /*5

 

2(3x-2)-2x-y=6x+1

5x+5y+x-y=1-4x

 

6x-4-2x-y-6x=1

6x+4y+4x=1

 

-2x-y=1+4

10x+4y=1

 

-2x-y=5         /*4

10x+4y=1

 

-8x-4y= 20

10x+4y=1

---------------

2x=21     /:2

 

x= 10,5

-2x-y=5        

 

x=10,5

-2*10,5-y=5

 

x=10,5

-21-y=5

 

x=10,5

-y=5+21

 

x=10,5

-y=26   /*-1

 

x=10,5

y= -26