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Here is a set of five equations:
b+c+d+e=4\\ a+c+d+e=5\\ a+b+d+e=1\\ a+b+c+e=2\\ a+b+c+d=0
What do you notice when you add the five equations?
Can you now find the values of a, b, c, d and e?
Here is a different set of equations:
xy = 1\\ yz = 4\\ zx = 9
What do you notice when you multiply the three equations given above?
Can you now find the values of x, y and z?
Is there more than one possible set of values?
Here is a third set of equations:
ab = 1\\ bc = 2\\ cd = 3\\ de = 4\\ ea = 6
Can you find all the sets of values {a, b, c, d, e} that satisfy these equations?
Extension
You may like to have a go at Overturning Fracsum.
Can you create your own set of symmetrical equations?
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?