it is solving a problem with three variables the question is

Question

3x+y-6z=17

4x+6y-5z=9

5x-6y+4z=-6

Answer 1

Elimnation method

Given equations are 3x+y-6z = 17 ------>(1)

4x+6y-5z = 9 ------> (2)

5x-6y+4z = -6 ------> (3)

To eliminate the y variaible, add the equations (2)&(3)

4x+6y-5z = 9 ------> (2)

5x-6y+4z = -6 ------> (3)

_______________________

9x-z = 3 -----> (4)

Multiple to each side of equation (1) by 6.

18x+6y-36z = 102 -------> (5)

To elminate the y variable Substitute the equation (2)from (5).

18x+6y-36z = 102

 4x+6y-5z = 9

(-)  (-)  (+)    (-)

________________

14x-31z = 93 -------> (6)

Multiple to each side of equation (4) by 31.

279x-31z = 93 ------> (7)

To elminate z variable subtract the equation (6) from (7).

279x-31z = 93

14x-31z = 93

(-)  (+)     (-)

_____________

-265x = 0

Divide to each side by negitive 265.

x = 0

Substitue x value in (4).

z = -3

Substitute x, z values in (1).

0+y+18 = 17

Subtract 18 from each side.

y = -1

Solution x = 0, y = -1, z = -3