Question

What is the solution to the following system? 4x+3y-z=-6 6x-y+3z=12 8x+2y+4z=6

A. x = 1, y = –3, z = –1
B. x = 1, y = –3, z = 1
C. x = 1, y = 3, z = 19
D. x = 1, y = 3, z = –2

Answer 1

b

Explanation:

Answer 2

Option B is correct.

Explanation:

4x+3y-z= -6 eq(1)

6x-y+3z= 12 eq(2)

8x+2y+4z=6 eq(3)

We need to solve these equations and find the value of x, y and z.

Multiply equation 2 with 3 and then add equation 1 and 2

18x -3y +9z = 36

4x +3y -z = -6

_____________

22x + 8z = 30 eq(3)

Multiply equation 2 with 2 and add with equation 3

12x -2y + 6z = 24

8x +2y +4z = 6

____________

20x + 10 z = 30 eq(4)

Multiply equation 3 with 10 and equation 4 with 8 and then subtract

220x + 80z = 300

160x + 80z = 240

- - -

_________________

60x = 60

x= 60/60

x= 1

Putting value of x in equation 3

22x + 8z = 30

22(1) + 8z = 30

8z = 30 - 22

8z = 8

z = 8/8

z=1

Putting value of x and z in equation 1

4(1)+3y-(1)=-6

4 + 3y -1 = -6

3 + 3y = -6

3y = -6 -3

3y = -9

y = -3

so, Option B x=1, y=3 and z=1 is correct