how to solve systems of of three variables equations using elimination?

Question

-x - 5y - 5z=2

4x- 5y+4z=19

x+5y-z=-20

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Answer 1

Elimination method

Given equations are -x-5y-5z = 2 ---> (1)

4x-5y+4z = 19 ---> (2)

x+5y-z = -20 ---> (3)

To eliminate the x , y  values add the equations (1)&(3).

-x-5y-5z = 2

x+5y-z = -20

_______________

-6z = -18

Divide to each side by negitive 6.

⇒ z = 3.

Substitute z  value in (2)&(3).

4x-5y+12 = 19

Subtract 12 from each side.

4x-5y = 7 ---> (4)

x+5y-3 = -20

Add 3 to each side.

x+5y = -17 ---> (5)

To eliminate y  value add the equations (4)&(5).

4x-5y = 7

x+5y = -17

______________

5x = -10

Divide to eachside by 5.

⇒ x = -2

Substitute the x  value in (5).

-2+5y = -17

Add 2 to each side.

5y = -15

Divide to each side by 5.

⇒ y = -3

Solution x = -2, y = -3 and z = 3.