Question

Which one of the following conditions must $p,q$ and $r$ satisfy so that the following systems of linear simultaneous equations has at least one solution such $p+q+r$ $\ne$ 0 ?
$x+2y-3z=p$;

$2x+6y-11z=q$;

$x-2y+7z=r$

• A. $5p+2q+r=0$
• B. $5p+2q-r=0$
• C. $5p-2p-r=0$
• D. $5p-2q+r=0$

Answer 1

The correct option is C $5p-2p-r=0$

Eliminating z form the 1st and 2nd equation and from the 2nd and the 3rd equation we get
$5x+4y=11p-3qand5x+4y=\frac{7q+11r}{5}$
At least one solution means we can have infinite solution Applying the conditions of infinite
solutions we get $11p-3q=\frac{7q+11r}{5}\Rightarrow 5p-2q-r=0$