Question 121707
1.{{{3x-6y=9}}}
2.{{{x-2y=3}}}
I think the easiest way to graph is to find the x and y intercepts. 
Find the intercepts.
Plot them. 
Draw the line. 
Start with Equation 1. 
1.{{{3x-6y=9}}} 
When y=0, then
{{{3x-6(0)=9}}}
{{{x=3}}}
First point (3,0)
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle( 3,0, .2 ))}}}
When x=0, then
{{{3(0)-6y=9}}}
{{{y=-3/2}}}
Second point (0,-3/2)
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle( 3,0, .2 ),circle(0,-3/2,.2))}}}
Then draw the line containing the two points. 
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle( 3,0, .2 ),circle(0,-3/2,.2),green(line( -10, -6.5, 10, 3.5)))}}}
Now continue with Equation 2.
2.{{{x-2y=3}}}
When y=0, then
{{{x-2(0)=3}}}
{{{x=3}}}
First point (3,0)
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle(3,0,.2),circle( 3,0, .15 ),circle(0,-3/2,.15),green(line( -10, -6.5, 10, 3.5)))}}}
When x=0, then
{{{0-2y=3}}}
{{{y=-3/2}}}
Second point (0,-3/2)
As you can see, the two lines have the same x and y intercepts.
They are the same line.
They are a linearly dependent system of equations and  they have an infinite number of solutions.