find ordered triple of thsese equations. 4x+6y+8z=-10, 4x+2y-6z=8, 2x+8y-6z=0

Question

which ordere4d triple is a solution of the system of equations?

Answer 1

Elimination method

Given equations 4x+6y+8z = -10 ----> (1)

4x+2y-6z = 8 ----> (2)

2x+8y-6z = 0 -----> (3)

To eliminate the x value, subtract the equation (2) from (1).

4x+6y+8z = -10

4x+2y-6z  = 8

(-) (-)  (+)     (-)

_______________

4y+14z = -18 ----> (4)

Multiple to each side of equation 2x+8y-6z = 0 by negitive 2.

-4x-16y+12z = 0 -----> (5)

To eliminate x value add the equations (2)&(5).

-4x-16y+12z = 0

4x+2y -6z   = 8

______________

-14y+6z = 8 -----> (6)

Multiple to each side of above equation by 4.

-56y+24z = 32 -----> (7)

Multiple to each side of equation 4y+14z = -18 by 14.

56y+196z = -252 ----> (8)

To eliminate the y value, add the equations (7)&(8).

-56y+24z = 32

56y+196z = -252

_______________

 220z = -220

Divide to each side by 220.

220z/220 = -220/220

z = -1

Substitute the z value in (4).

4y-14 = -18

4y = -4

Divide to each side by 4.

y = -1

Substitute the y,z value in (3).

2x-8+6 = 0

2x-2 = 0

Add 2 to each side.

2x = 2

Divide to each side by 2.

x = 1

Orderd triple of above equations (x,y,z) = (1,-1,-1)