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Unique, none or infinitely many solutions

Unique, none or infinitely many solutions

IP 1
7 marks
  1. Solve the simultaneous equations \(2x+3y=6\) and \(4x+5y=14\).[2]
  2. Explain why the simultaneous equations \(2x+3y=6\) and \(4x+6y=15\) have no solution, and describe their graphs.[2]
  3. Find the value of \(k\) for which \(2x+3y=6\) and \(4x+6y=k\) have infinitely many solutions, and describe these solutions.[2]
  4. Find the value of \(p\) for which \(2x+3y=6\) and \(px+6y=10\) have no solution.[1]

Solution:

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Answer:(a) \(x=6\), \(y=-2\) (b) doubling the first gives \(4x+6y=12\ne15\); parallel lines (c) \(k=12\); every point of the line \(2x+3y=6\) (d) \(p=4\)

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