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
$x-2y=8$
$5x-10y=10$

Answer 1

Slope of $1^{st}$ line =$-\frac{1}{-2}=\frac{1}{2}$

Slope of $2^{nd}$ line =$-\frac{5}{-10}=\frac{1}{2}$

$\Rightarrow$both lines have the same Slope

Divide equation (2) by 5;

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

$\therefore$The two lines are parallel

$\Rightarrow$The system has no solution