Question
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Solve for and simultaneously :
and

Ask by Frank Macdonald. in South Africa
Mar 15,2025

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Tutor-Verified Answer

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.
  1. From the second equation , we can express in terms of :
  2. Substitute this expression for into the first equation:
    Simplifying gives :
  3. Expand both squares:
  4. Combining these gives:
  5. Subtracting 4 from both sides:
  6. Now we can use the quadratic formula with :
  7. Thus, we have two possible values for :
  8. Now, substitute these values back into to find the corresponding values:
    For :
    For :
  9. So the solutions are:
Thus, the values of are:

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