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Question 70914: Solve the following systems by graphing.
x - 2y = 8
3x - 2y = 12
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 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.
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