Question

The equations $2x+4y+z=0,x+2y-2z=5,3z+6y+7z=2$ have:

• A. unique solutions
• B. no solution
• C. infinite number of solutions
• D. two solutions

Answer 1

The correct option is B no solution

The coefficient Matrix.
$A=\left|\begin{array}{ccc}2& 4& 1\\ 1& 2& -2\\ 3& 6& 7\end{array}\right|$
$|A|=2(14+12)-4(7+6)+1(6-6)$
$=52-52=0$
Now take $x=0$in eq (1) & eq (2)
$4y+2=0$
$2y-22=5$
on solving we get $z=-2y=1/2x=0$
Put this in equation (3)
$\Rightarrow 3\left(0\right)+6\left(1/2\right)+7(-2)$
$\Rightarrow 3-14$
$\Rightarrow -11\ne 2.$
$\therefore$ No solution