Question

What is the solution to the system of equations?

-3x-4y+z=-1
2x+y-z=-8
x+8y-z=23

A. (-3,4,6)
B. (4,-3,-1)
C. (-3,4,8)
D. (3,-4,-6)

Answer 1

The answer is A (-3,4,6).

Explanation:

1 Solve for z in -3x-4y+z=-1

z=3x-1+4y

2 Substitute z=3x-1+4y into 2x+y-z=-8

-x-3y+1=-8

3 Substitute z=3x-1+4y into x+8y-z=23

-2x+4y+1=23

4 Solve for x in -x-3y+1=-8

x=-3y+9

5 Substitute x=-3y+9 into z=3x-1+4y

z=-5y+26

6 Substitute x=-3y+9 into -2x+4y+1=23

10y-17=23

7 Solve for y in 10y-17=23

y=4

8 Substitute y=4 into z=-5y+26

z=6

9 Substitute y=4 into x=-3y+9

x=-3

10 Therefore,

x=-3

y=4

z=6