Question 70914
To solve this system of equations by means of graphing you draw each graph and then 
identify the point where the two graphs cross.  The x and y values at that point are the
values of x and y that will satisfy both equations.
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The two equations to graph are:
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x - 2y = 8
3x - 2y = 12
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You can graph the equations if you can find two points for each equation. An easy way to
to this is pick one of the equations. Set x equal to zero (making the x term disappear)
and then solve for y.  In the first (top) equation above, setting x equal to zero 
eliminates the x term and the equation becomes -2y = 8.  Solve by dividing both sides
by -2 to get y = -4.  So we know that when x = 0 then y = -4.  This means that the point
(0,-4) is on the graph.  Next we can do the same sort of thing only this time let
y equal zero.  The term containing y disappears and the equation reduces to x = 8. So
the point (8, 0) is also on the graph.  Plot these two points and draw a line through
them and beyond in both directions. That completes the graph for the first equation.
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Do the same sort of procedure for the second equation.  Set x equal to zero, making 
the term containing x disappear and leaving the equation -2y = 12.  Divide both sides
of this equation by -2 to find that y = -6.  This makes a point that is on this graph
(0, -6).  Return to the original equation and set y equal to zero. The term containing
y disappears and you are left with 3x = 12.  Divide both sides by 3 to find that x = 4.
So we know that (4, 0) is also on this second graph.  Plot the two points (0, -6) and 
(4, 0) and then draw a line through them and beyond.  
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If you have graphed accurately you should now see the point where the two graphs cross.
Find the x and y values for that point and they should satisfy both of the equations.
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As a check you should find that the common or crossing point for the two graphs is (2, -3).
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Hope this helps you to understand graphing of linear equations for the purpose of finding
a common solution to the set of equations.