Question 55674
These equations are easier to graph if you put them into the slope-intercept form: y = mx+b

{{{2x-6y = 9}}}  Add 6y to both sides.
{{{2x = 6y+9}}}  Subtract 9 from both sides.
{{{2x-9 = 6y}}}  Finally, divide both sides by 6.
{{{(2/6)x - 9/6 = y}}} Simplify.
{{{y = (1/3)x - 3/2}}}
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{{{x - 2y = 3}}}  Add 2y to both sides.
{{{x = 2y+3}}}  Subtract 3 from both sides.
{{{x - 3 = 2y}}}  Finally, divide both sides by 2.
{{{(1/2)x - 3/2 = y}}} or
{{{y = (1/2)x - 3/2}}}

The graphs are:
{{{graph(300,200,-5,5,-5,5,(1/3)x-(3/2),(1/2)x-(3/2))}}}

As you can see from the graph, the two lines intersect at the point (0, -2/3) so this is the solution.
But also notice that both equations, in their slope-intercept form, have the same y-intercept (that's the b in y = mx+b) which is (0, -2/3).