Question

In the following given systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it
$x-3y=3$
$3x-9y=2$

Answer 1

Slope of $1^{st}$ line =$-\frac{1}{-3}=\frac{1}{3}$

Slope of $2^{nd}$ line =$-\frac{3}{-9}=\frac{1}{3}$

$\Rightarrow$both lines have the same Slope

And when we divide $2^{nd}$ equation by $3$;

$\Rightarrow$equation (2) : $x-3y=2/3$, which differ by constant from that of 1st equation

$\therefore$The two lines are parallel

$\Rightarrow$lines have no solution