Question

The system of equations $x+y+z=2,3x-y+2z=6$ and $3x+y+z=-18$ has

• A. A unique solution
• B. No solutions
• C. An infinite number of solutions
• D. Zero solution as the only solution

Answer 1

The correct option is A A unique solution

Given system of equation can be written as $\left[\begin{array}{ccc}1& 1& 1\\ 3& -1& 2\\ 3& 1& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}2\\ 6\\ -18\end{array}\right]$
On solving the above system we get the unique solution x = -10, y = -4, z = 16.