Question 58032
Hi Sher,
This is a dependent system.  If you tried to eliminate either variable you'd eliminate them both and get 0=0.  I told you about that on the last question I answered.  That means that graphically these to equations are represented by the same line.  I didn't garph the last system, I can add a graph to that answer if you need it.  Let me know.
:
L1) 3x - 6y = 9
L2)  x - 2y = 3
:
For L1, let x=0 and solve for y:
3(0)-6y=9
-6y=9
-6y/-6=9/-6
y=-3/2
Plot (0,-3/2)
Now, let y=0 and solve for x:
3x-6(0)=9
3x=9
3x/3=9/3
x=3
Plot (3,0)
Connect the points and you have this line:
{{{graph(300,200,-10,10,-10,10,(-3x+9)/-6)}}}
For L2), let x=0 and solve for y:
(0)-2y=3
-2y=3
-2y/-2=3/-2
y=-3/2
Plot (0,-3/2)  Notice that it's right on top of the other line's y-intercept.
Let y=0 and solve for x:
x-2(0)=3
x=3
Plot (3,0)  Notice that it's right on top of L1)'s x-intercept.
Connect the points and you have a line right on top of another line.  
The graph below has both lines graphed, but you can only see one because graphically they are the same line.
{{{graph(300,200,-10,10,-10,10,(-3x+9)/-6,(-x+3)/-2)}}}
Happy Calculating, Sher!!!