Question

1. Rozwiąż układ równań metodą podstawiania :

a )

-x +5y = 6

x - 3y = -4 całe w klamerce

b )

3x + y =3

2x -3 y = 2

Answer 1

a)

-x + 5y = 6

x - 3y = -4

 

-x + 5y = 6

x = 3y - 4

 

-(3y - 4) + 5y = 6

  x = 3y - 4

 

-3y + 4 + 5y = 6

  x = 3y - 4

 

2y = 6 - 4

  x = 3y - 4

 

2y = 2

  x = 3y - 4

 

y = 1

x = 3*1 - 4

 

y = 1

x = -1

 

 

b)

 

3x + y = 3   

2x - 3y = 2 

 

y = 3 - 3x

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

 

 y = 3 - 3x

2x - 9 + 9x = 2

 

 y = 3 - 3x

11x =  2 + 9

 

 y = 3 - 3x

11x = 11

 

 y = 3 - 3x

x = 1

 

y = 3 - 3*1

x = 1

 

y = 3 - 3

x = 1

 

y = 0

x = 1 

 

Answer 2

Metoda podstawiania.

a)

(1) -x+5y = 6

(2) x-3y = -4  => x = 3y-4

 

z (2) podstawiamy do (1)

-(3y-4)+5y = 6

x-3y = -4

 

-3y+4+5y = 6

x-3y = -4

 

-3y+4+5y = 6

x-3y = -4

 

2y = 6-4

x-3y = -4

 

2y = 2

y = 1

------

x-3*1 = -4

x = -4+3

x = -1

 

{x = -1}

{y = 1}

 

b)

(1)  3x+y = 3   => y = 3-3x

(2)  2x-3y = 2

 

y = 3-3x

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

 

y = 3-3x

2x-9+9x = 2

 

y = 3-3x

11x = 2+9

 

y = 3-3x

11x = 11  /:11

 

y = 3-3x

x = 1

------

y = 3-3*1 = 3-3 = 0

 

{x = 1}

{y = 0}