Solving Systems of Equations by Elimination?

Question

-x - 5y - 5z = 2 4x - 5y + 4z = 19 x + 5y - z = -20 or -x - 5y + z = 17 -5x - 5y + 5z = 5 2x + 5y - 3z = -10

Answer 1

Let -x - 5y - 5z = 2 be ( Eq. 1 ), 4x - 5y + 4z = 19 be ( Eq. 2 ) and x + 5y - z = -20 be ( Eq. 3 ).

Add ( Eq. 1 ) and ( Eq. 2 ) to eliminate x and y, that is:

- 6z = - 18

z = 3

Substract ( Eq. 1 ) and ( Eq. 2 ) to get ( 4 ) and to eliminate y, and that is:

- 5x - 9z = - 17 ( 4 )

Substitute the value of z to ( Eq. 4 ), that is:

- 5x - 9 ( 3 ) = - 17

- 5x = 10

x = - 2

Substitute the value of x and z to ( Eq. 1 ) to get the value of y, and that is:

4 ( - 2 ) - 5y + 4 ( 3 ) = 19

- 8 - 5y + 12 = 19

- 5y = 15

y = - 3

Thus, the value of x, y, and z is 2, - 3, and 3, respectively.