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Answer
The solutions are
and
.
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The Deep Dive
To solve the equations simultaneously, we start with the first equation, which represents a circle with a center at (2, 3) and a radius of 2. The second equation is a straight line.
-
From the second equation
, we can express in terms of : -
Substitute this expression for
into the first equation: Simplifyinggives : -
Expand both squares:
-
Combining these gives:
-
Subtracting 4 from both sides:
-
Now we can use the quadratic formula
with : -
Thus, we have two possible values for
: -
Now, substitute these values back into
to find the corresponding values: For: For: -
So the solutions are:
Thus, the values of
are: