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Intersections
Age 14 to 18
Challenge Level 
Why do this problem?
On the one hand this problem is a simple exercise in solving pairs of linear simultaneous equations but on the other it provides perhaps unexpected results that call for investigating the connection between the algebra and geometry, and considering the equations of the lines and gradients.
Possible approach
Set this as homework or as a lesson starter and have a class discussion about the results.
Key questions
Why are the solutions of the two pairs of simultaneous equations so different when the equations are so nearly the same?
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Real(ly) Numbers
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?
