Question

What is the solution to the system?

{x+3y-z=6
{4x-2y+2z= -10
{6x+z= -12


A. (2, 1, -3)
B. (-3, 5, 6)
C. (0,-2,-12)

Answer 1

B. (-3, 5, 6)

Explanation:

The system of equations is:

x + 3y - z = 6 ... (i)

4x - 2y + 2z = -10 ... (ii)

6x + z = -12 ... (iii)

The value of z in (iii) is;

z = -12 - 6x

Replacing z in (i) and (ii) gives:

x + 3y - (-12 - 6x) = 6 ... (i)

4x - 2y + 2(-12 - 6x) = -10 ... (ii)

Simplifying gives;

7x + 3y = -6 ... (i)

-8x - 2y = 14 ... (ii)

Multiplying (i) by 2 and (ii) by 3 gives;

14x + 6y = -12 ... (i)

-24x - 6y = 42 ... (ii)

Adding (i) and (ii) gives;

-10x = 30

x = -3

Replacing x = -3 in (i) gives;

7(-3) + 3y = -6

3y = 21 - 6

y =
`(15)/(3)` = 5

Replacing x = -3 in (iii) gives;

6(-3) + z = -12

z = -12 + 18 = 6