Answer:
B. (-3, 5, 6)
Step-by-step 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 = [tex]\frac{15}{3}[/tex] = 5
Replacing x = -3 in (iii) gives;
6(-3) + z = -12
z = -12 + 18 = 6
