Question

Solve the system using the elimination method.  −8x− 4y+ 2z  = −26 , −2x+ 4y+ 2z  = 10 and  −6x − 8y − 5z  = −41

Answer 1

Elimination method

Given -8x-4y+2z = -26 ------> (1)

-2x+4y+2z = 10 ------> (2)

-6x-8y-5z = -41 -------> (3)

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

-4x+8y+4z = 20 --------> (4)

To eliminate the y value add the equations (1) and (2).

-8x-4y+2z = -26

-2x+4y+2z = 10

_______________

-10x+4z = -16 ------> (5)

To eliminate the y value add the equations (3) and (4).

-6x-8y-5z = -41

-4x+8y+4z = 20

______________

-10x-z = -21 -------> (6)

To eliminate the x value subtract equation (6) from (5).

-10x+4z = -16

-10x-z = -21

(+)   (+)      (+)

_____________

5z = 5

⇒ z = 1

Substitute the z value in (6).

-10x-1 = -21

-10x = -20

-10x/-10 = -20/-10

⇒ x = 2

Substitute the x,z in (1)

-8*2-4y+2*1 = -26

-16-4y+2 = -26

-14-4y = -26

-4y = -26+14

-4y = -12

-y = -12/-4

⇒ y = 3

Solution is x = 2, y = 3, z = 1.