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Question 84499: How and what do I do?Please help me?
Solve the system by graphing.
3x – y = 1
3x – y = 2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let me start by saying that these two equations have no common solution. You can tell that
because when you graph them their graphs turn out to be parallel lines. In order for linear
equations such as these to have a common solution, their graphs must cross at some point.
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You can get points on each of the graphs easily. For the first equation:
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3x - y = 1
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one point could be found by setting x equal to zero. When you do that, the equation
becomes - y = 1. Solve for y by multiplying both sides by -1 to get y = -1. This tells
you that (0, -1) is a point on the graph. When you plot this point, you will find that it
is on the y-axis. [by setting x = 0, the answer for y will be on the y-axis.]
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Another point on the graph can be found by setting y = 0. When you do that the equation
reduces to 3x = 1. Solve for x by dividing both sides by 3 and you get x = 1/3. In this
case since x = 1/3 when y = 0, you know the point (1/3, 0) is on the graph. Note that when
you plot this point you will find that it is on the x-axis. [by setting y equal to zero,
the answer for x will be on the x-axis.]
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Plot those two points (0, -1) and (1/3, 0) and extend a straight line that runs through
them and you have the graph of the first equation.
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You can get two points for the second equation in the same way. In the second equation:
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3x - y = 2
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You can set x equal to zero and solve for y to find that y = -2. So the point (0, -2) is
on the graph of the second equation.
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Then set y = 0 and solve for x to find that the point (2/3, 0) is also on the graph of
the second equation.
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Plot these two points and extend a straight line through them to complete the graph of
this equation.
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Your graphs should now look like this:
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Notice that the "brown" graph is for the first equation because it crosses the y-axis
where y equals -1 and the "green" graph is for the second equation because it crosses
the y-axis at -2.
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Notice that the lines are parallel, so they will never cross. Therefore, there is no common
solution for the two equations.
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Hope this helps you to understand the process of finding a common solution (or lack of
a common solution) by using the method of graphing.
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