Question

Rozwiąz układ z trzema niewiadomymi

3x-2y+z= -3

4x+y+2z=2

-2+5y-3z=14

Answer 1

3x - 2y + z = -3

 

4x + y + 2z = 2 / *5

 

-2 + 5y - 3z = 14

 

z  = -3 -3x + 2y

4x + y + 2z = 2

 

-2 + 5y - 3z = 14

 

z = -3 -3x + 2y

4x + y + 2(-3 -3x +2y) = 2

-2 + 5y - 3(-3 -3x +2y) = 14

 

z = -3 -3x + 2y

4x + y - 6 - 6x + 4y = 2

-2 + 5y + 9 + 9x - 6y = 14

 

z = -3 -3x + 2y

-2x + 5y - 6 = 2

9x - y + 7 = 14 /*5

 

-2x + 5y - 6 = 2

45x - 5y + 35 = 70  +

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

43x  + 29 = 72

43x = 72 - 29

43x = 43

x = 1

 

z = -3 -3*1 + 2y

-2*1 + 5y - 6 = 2

 

z = -3 - 3 + 2y

-2 + 5y - 6 = 2

 

z = -6 + 2y

5y - 8 = 2

 

 

z = -6 + 2y

5y = 2 + 8

 

z = -6 + 2y

5y = 10

 

z = -6 + 2y

y = 2

 

z = -6 + 2 * 2

z = -6 + 4

z = -2

 

x =1

y =2

z = -2