Question

The system $x+4y-2x=3,3x+y+5x=7$ and $2x+3y+z=5$ has

• A. Infinite number of solutions
• B. Unique solution
• C. Trivial solution
• D. No solution

Answer 1

The correct option is D No solution

$x+4y-2x=3$

$3x+y+5x=7$

$2x+3y+z=5$

$\Delta =\left|\begin{array}{ccc}1& 4& -2\\ 3& 1& 5\\ 2& 3& 1\end{array}\right|$

$=1(1-15)-3(4+6)+2(20+2)$

$=-14-30+44$

$=0$

${\Delta }_3=\left|\begin{array}{ccc}1& 4& 3\\ 3& 1& 7\\ 2& 3& 5\end{array}\right|$

$=1(5-21)-3(20-9)+2(28-3)$

$=-16-33+50$

$=1$

$\Delta =0$ but ${\Delta }_3\ne 0$

So, no solution.