Question

Show graphically that the following given system of the equation has infinitely many solutions:
$3x-y=5,6x-2y=10$

Answer 1

$3x-y=5$....(1)
$6x-2y=10$......(2)
Isolate $x$ from equation (1) and find the value of $x$ and $y$.
$3x-y=5$
or $y=3x-5$

At,

$x$	$y$
$0$	$-5$
$1$	$-2$
$3$	$4$

Similarly, isolate $x$ from equation (2) and find the values of $x$ and $y$.
$6x-2y=10$

or $y=(6x-10)/2$

At,

$x$	$y$
$2$	$1$
$4$	$7$
$3$	$4$

Using the above points and plotting the Graph we get,
Both the lines coincide with each other that means that system has infinite many solutions.