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This is equivalent to solving the simultaneous equation set {x, y: x + y = 6, xy = 7}.
By rearranging and substituting, we find that x = 6 - y, and that (6 - y)y = 7.
We can expand and simply to gain -y2 + 6y - 7 = 0, a relatively simple equation called a quadratic, and one which has a precise formula for its solution.
Using this formula, we find that y = 1.586 and y = 4.414. Note that because these add to six, we will end up with the same answers for x, i.e. for y = 1.586, x = 4.414 and ice versa.
Regardless of the way you choose to then label the numbers, the solution is (1.586, 4.414). These add to 6 and multiply to 7.
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the correct answer
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the correct answer
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