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Solutions that depend on a parameter

Solutions that depend on a parameter

IP 1
6 marks

For a constant \(k\), the simultaneous equations are \(x+y=k\) and \(x-y=2\).

  1. Solve the equations, giving \(x\) and \(y\) in terms of \(k\).[2]
  2. Find the value of \(k\) for which \(x=2y\).[2]
  3. Find all the values of \(k\) for which \(x\) and \(y\) are both positive integers.[2]

Solution:

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Answer:(a) \(x=\dfrac{k+2}{2}\), \(y=\dfrac{k-2}{2}\) (b) \(k=6\) (c) every even integer \(k>2\)

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