Question

if (a,a + square root 3) lies on the graph of y=2x, then a = ?

Answer 1

Start with y = 2x.  Subst. a for x and a+sqrt(3) for y:

a+sqrt(3) = 2a

Subtracting a from both sides:  sqrt(3) = a

Answer 2

If the point
$(a \: \: a \sqrt{3} )$
lies on
$y = 2x$
then it must satisfy it.

That is

$a + \sqrt{3} = 2(a)$
$\rightarrow \: a + \sqrt{3} = 2a$


Grouping like terms we have,

$\sqrt{3} = 2a - a$
$\therefore \: a = \sqrt{3}$