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Question 70913: Solve the following systems by graphing.
2x - y = 4
2x - y = 6
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 2x - y = 4
2x - y = 6
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Let's put these equations into the slope intercept form of y = mx + b where m is the slope
of the graph and b is the point where the graph crosses the y-axis.
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The first equation can be put into slope intercept form in two steps. First subtract
2x from both sides of the equation to get -y = -2x + 4. Then multiply the entire equation
by -1 to get the slope intercept form of y = 2x -4. This tells you that the graph crosses the
y-axis at -4, a point designated by (0, -4). You can easily get another point on the graph
by returning to the original equation and setting y equal to zero. This reduces the
equation to 2x = 4 which after dividing both sides by 2 becomes x = 2. So the point
(2, 0) is also on the graph. You can plot the two points (0, -4) and (2, 0) and draw a line
through them to see what the graph looks like. And you also know the slope of the line
is +2 because in the slope intercept form that is the multiplier of the x term.
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You can do a similar analysis for the second equation. Put it into slope intercept
form. Do that by subtracting 2x from both sides to get -y = -2x + 6. Multiply this entire
equation by -1 to get the slope intercept form of y = 2x - 6. This tells you that the graph
has a slope of +2 and crosses the y-axis at -6. And a y-axis crossing at -6 can be written
as the point (0, -6). You can again find another point on the graph by returning to the
original equation and setting y equal to zero. When you do the equation reduces to
2x = 6 and dividing by 2 determines that x = 3. So the point (3, 0) is also on this graph.
Plot the points (0, -6) and (3,0) and draw a line through them.
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You should now see from the graphs that the lines look parallel. In fact, they have to
be parallel because they both have the same slope of +2, the difference being that one
graph crosses the y-axis at -4 and the other at -6.
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The thing that is critical is that parallel lines never cross. And a crossing point of
linear graphs is the common solution for the system. Therefore, this given set of equations
has no common solution ... trick question.
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Hopefully this helps to give you a little more understanding of graphing linear equations
and associating the equations with the graphs.
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