Question

The system of equations $x-2y+3z=5,2x-2y+z=0,-x+2y-3z=6$ has

• A. infinitely many solutions
• B. exactly two solutions
• C. unique solution
• D. no solution

Answer 1

Answer: (D)

Given system of equations,
$x-2y+3z=5$ ...(i)
$2x-2y+z=0$ ...(ii)
$-x+2y-3z=6$ ...(iii)
$\because \Delta =\left|\begin{array}{ccc}1& -2& 3\\ 2& -2& 1\\ -1& 2& -3\end{array}\right|$
$=1(6-2)+2(-6+1)+3(4-2)$
$=4-10+6=0$
${\Delta }_1=\left|\begin{array}{ccc}5& -2& 3\\ 0& -2& 1\\ 6& 2& -3\end{array}\right|$
$=5(6-2)+2(0-6)+3(0+12)$
$=20-12+36\ne 0$
So, no solution.