Question

zad.1.

Rozwiąż metodą podstawiana

a) 2x+y=3

x+y=2

b) x-y=3

4x+2y=6

c)3x-y+2=0

x+2y=-3

d) x+2y-3=-3

x+y+2=0

Answer 1

a) 2x+y=3

x+y=2

 

y= 3 - 2x

x + 3 - 2x = 2

 

y= 3 - 2x

x - 2x = 2 - 3

 

y= 3 - 2x

-x = -1 /: (-1)

 

y= 3 - 2x

x= 1

 

y= 3 - (2 *1)

x= 1

 

y= 3 - 2

x= 1

 

y= 1

x= 1

 

b) x-y=3

4x+2y=6

 

x= 3 + y

4 (3+y) + 2y = 6

 

x= 3 +y

12 + 4y + 2y = 6

 

x= 3 + y

6y = 6 - 12

 

x= 3 + y

6y = -6 /:6

 

x= 3 + y

y= -1

 

x= 3 + (-1)

y= -1

 

x= 2

y= -1

 

c)3x-y+2=0

x+2y=-3

 

3x - y = -2

x + 2y = -3

 

-y = -2 - 3x /: (-1)

x + 2y = -3

 

y = 2 + 3x

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

 

y= 2 + 3x

x + 4 + 6x = -3

 

y= 2 + 3x

7x = -3 - 4

 

y= 2 + 3x

7x = -7 /: 7

 

y= 2 + 3x

x = -1

 

y= 2 + 3 (-1)

x = -1

 

y= -1

x = -1

 

d) x+2y-3=-3

x+y+2=0

 

x + 2y = 0

x + y = -2

 

x = 0 - 2y

0-2y + y = -2

 

x= 0 - 2y

-y = -2 /: (-1)

 

x= 0 - 2y

y= 2

 

x= 0 - 2* 2

y= 2

 

x= -4

y = 2

Answer 2

a)

y=3-2x

x+3-2x=2

 

x=1

y=3-2

 

x=1

y=1

 

(1,1)

 

b)

x= 3+y

12+6y=6

y= -1

x= 3-1

 

x=2

y=-1

(2,-1)- NIE ZAPOMNIJ O TYM !

 

c)

x=-3 - 2y

(-3-2y)*3-y+2=0

-9-6y-y+2=0

 

y=1

x=-3-2

x=-5

 

x=-5

y=1

(-5,1)

 

d)

x=2y

3y+2=0

y= -2/3

x=-1 i 1/3

 

x=-1 i 1/3

y= -2/3

(-1 i 1/3, -2/3)

Myślę, że dobrze. Proszę naj :)