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
$2x+y=5$
$4x+2y=10$

Answer 1

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

Slope of $2^{nd}$ line =$-\frac{4}{2}=-2$

$\Rightarrow$ Slope of 1st line =Slope of $2^{nd}$ line

Divide $2^{nd}$ equation by 2;

$\Rightarrow$equation (2) : $2x+y=5$, which is identical to 1st equation

$\Rightarrow$both lines coincide with each other

$\therefore$ The system has infinitely many solutions