Question 103229
First we need to put each equation in slope intercept form
Slope intercept form is:
y = mx + b
m is the slope and
b is y intercept
Ok so the first equation is:
x - 2y = 8
first go ahead a place a 1 in front of the x
this is just a good way to remember that it is there (x=1*x=1x)
1x - 2y = 8
now move the 1x over by subtracting it from both sides
1x - 1x - 2y = -1x + 8
the 1x's on the right side cancel out leaving 
-2y = -1x + 8
now divide both sides by -2
-2y/-2 = -1x/-2 + 8/-2
{{{y = (1/2)x - 4}}}
now we have the equation in slope intercept form y = mx + b
and we can easily see that
slope is {{{1/2}}}
and the y intercept is -4
Now we are ready to graph this line
Start at the y intercept 
The y intercept is where the line crosses the y axis so this is a known point on the line we are trying to graph.
Since we know that the y intercept for this line is -4
move your pencil to point (0,-4) and mark a dot on the graph
Now lets look at the slope 
slope is defined as {{{rise/run}}}
The slope for this line is {{{1/2}}}
so we are going to rise up 1 and run to the right 2
Place your pencil over the dot we just marked at point (0,-4)
and rise up 1 
you should be at point (0,-3) on the graph
now run to the right 2
you should be at point (2,-3) on the graph
mark a dot here.
Now using a ruler line up the dots and draw a line through them.
Here is what your graph should look like.

{{{ graph( 500, 500, -10, 10, -10, 10, (x/2)-4) }}} 
Now lets graph the second equation
3x - 2y = 12
Follow the same steps as we did for the first equation
first put the equation in slope intercept form
3x - 2y = 12
3x - 3x - 2y = -3x + 12
-2y = -3x + 12
-2y/-2 = -3x/-2 + 12/-2
{{{y = (3/2)x-6}}}
Ok so the slope for this line is {{{3/2}}}
and the y intercept is -6
Lets graph it.
Again use the same steps as we did for the first line
start at the y intercept for this line
mark a dot at point (0,-6)
and the slope for this line is {{{3/2}}}
so from point (0,-6)
rise up 3
and run to the right 2
you should be at point (2,-3) on the graph 
using a ruler draw a line through both points 
now your graph should look like this.
{{{ graph( 500, 500, -10, 10, -10, 10, (x/2)-4, (3x/2)-6) }}} 
The point at which the lines intersect is the solution for this system of equations.
the point of intersection is (2,-3)
<b>This means that for this system of equations x = 2 and y = -3</b>
Lets check these solutions in the original equations
first equation:
x - 2y = 8
substitute x with 2 and y with -3
2 - 2(-3) = 8
2 + 6 = 8
8 = 8
Ok now try the second equation
3x - 2y = 12
3(2) - 2(-3) = 12
6 + 6 = 12
12 = 12
Our solution satisfies both equations so we can be sure we have found the correct solution for this system of equations.