Solve the system, if possible.
A)x = -10, y = 7, z = 8
B)x = 3, y = 18, z = 8
C)x = 10, y = -7, z = -8
D)x = -6, y = 10, z = 8
E)no solution; inconsistent system

Question

Solve the system, if possible. 
A)x = -10, y = 7, z = 8 
B)x = 3, y = 18, z = 8 
C)x = 10, y = -7, z = -8 
D)x = -6, y = 10, z = 8 
E)no solution; inconsistent system

Quizplus · Accepted Answer

By substitution, the second equation becomes $2x-y=24.$ Adding this with the first equation gives $3x+z=16.$ Solving for $z$ in the third equation and substituting for $z$ in the fourth equation gives $x-y=6.$ Solving the system $$\begin{cases} 3x+z=16 \ x-y=6 \end{cases}$$ gives $x=4$ and $y=-2,$ and solving for $z$ in the third equation gives $z=-24-4+2=-26.$ Thus $(x,y,z)=(4,-2,-26),$ which matches (C).

Solve the System, If Possible