You can
put this solution on YOUR website!Graphing the first equation
In order to graph
, we need to solve for "y" first.
Start with the first equation.
Subtract
from both sides.
Rearrange the terms.
Divide both sides by
to isolate y.
Break up the fraction.
Reduce.
In order to graph this equation, we only need two points to create a straight line
--------------------------------Let's find the first point--------------------------------
Start with the given equation
Plug in
Multiply
and
to get
Subtract
So when
, we have the value
. This means we have the first point
)
--------------------------------Let's find the second point--------------------------------
Start with the given equation
Plug in
Multiply
and
to get
Subtract
So when
, we have the value
. This means we have the second point
)
------------------------------------------------------------------------------------------------
So we have the two points:
)
and
)
Now plot these two points on a coordinate system
Now draw a straight line through the two points. This line is the graph of
Graph of
through the two points
and
Graphing the second equation
Start with the second equation.
Subtract
from both sides.
Rearrange the terms.
Divide both sides by
to isolate y.
Break up the fraction.
Reduce.
Take note that this equation is EXACTLY identical to the equation we just plotted. So the graph of
(and
) is
Now graphing the two equations together gives you
Note: there are really two equations here. One is just right on top of the other (which hides it)
Since one equation is right on top of the other, this tells us that there are an infinite number of solutions (since there are an infinite number of intersections).
So the system is dependent.
