4x-3y+z=0, -2y-5z=6 and -4x+5y+2z=-2

Question

4x-3y+z=0

-2y-5z=6

-4x+5y+2z=-2

Answer 1

Elimination method :

Given equations are 4 x - 3 y +  z = 0 -------> (1)

- 2 y - 5 z = 6  --------> (2)

- 4 x + 5 y + 2 z = - 2-------> (3)

To eliminate the x  value add  (1 )&(3).

4 x - 3 y +  z = 0

- 4 x + 5 y + 2 z = - 2

_______________

2 y + 3 z  = - 2 ---------> (4)

 

To eliminate the y  value add (2)&(4).

- 2 y - 5 z = 6

2 y + 3 z  = - 2

_________________

- 2 z = 4

z = - 2.

Substitute the z value in eq ( 2 ).

- 2 y - 5 z = 6 

- 2 y - 5 (- 2  )= 6

- 2 y + 10 = 6  

- 2 y = 6 - 10

- 2 y = - 4

y = 2 .

Substitute the values z  & y values in eq ( 1 )

4 x - 3 y +  z = 0

4 x - 3 ( 2 ) + (- 2 )  = 0

4 x - 6 - 2 =  0

4 x - 8=  0

4 x = 8

x = 2.

Solution of the system of  the equations is x = 2 , y  = 2 and  z = - 2.