3x + 6y – 6z = 9, 2x – 5y + 4z = 6 and -x +16y + 14z = -3 what is the answer

Question

how do you solve it and what are the answers ?

Answer 1

Elimination method

Given equations 3x+6y-6z = 9 ---> (1)

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

-x+16y+14z = -3 ---> (3)

Multiple to each side of equation (3) by 2.

-2x+32y+28z = -6 ---> (4)

Multiple to each side of equation (3) by 3.

-3x+48y+42z = -9 ---> (5)

To eliminate the x value, add the equations (1)&(5).

-3x+48y+42z = -9

3x+6y-6z = 9

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54y+36z = 0 ---> (6)

To eliminate the x value, add the equations (2)&(4).

2x-5y+4z = 6

-2x+32y+28z = -6

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27y+32z = 0 ---> (7)

Multiple to each side of equation (6) by 32.

1728y+1152z = 0 ---> (8)

Multiple to each side of equation (7) by negitive 36.

-972y-1152z = 0 ---> (9)

To eliminate z value add the equations (8)&(9).

1728y+1152z = 0

-972y-1152z = 0

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756y = 0

⇒ y = 0

Substitute the y value in (1)&(3).

3x-6z = 9 ---> (10)

-x+14z = -3

Multple to each side by 3.

-3x+42z = -9 ---> (11)

To eliminate the x value add the equations (10)&(11).

3x-6z = 9

-3x+42z = -9

_____________

36z = 0

⇒ z = 0

Put y,z in (3).

-x+0+0 = -3

⇒ x = 3

Solution x = 3, y = 0, z = 0.