Question

Show that there is no solution for the equations
$x+4y-2z=3$
$3x+y+5z=7$
$2x+3y+z=5$.

Answer 1

(a) Here $△=\left|\begin{array}{ccc}1& 4& -2\\ 3& 1& 5\\ 2& 3& 1\end{array}\right|$

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

= $-14-30+44=0$

And ${△}_x=\left|\begin{array}{ccc}3& 4& -2\\ 7& 1& 5\\ 5& 3& 1\end{array}\right|=3(1-15)-7(4+6)+5(20+2)=-2\ne 0$

Since $△=0$ and ${△}_x\ne 0$, the equations are not consistent and hence there is no solution of the given system of equations.