Sum and Product SystemPro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear
Sum and Product System
The sum of a number and twice another number is ten less than the product of the numbers. The sum of the numbers is ten. What are all possible numbers that satisfy these criteria?
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Find all ordered pairs (x, y) such that the following two equations are true:
x2 - 4y2 = 108
x = 18 - 2y
Usually we say that if we have two variables, we need two equations to solve, and if we have three variables, we need three equations to solve. This is not 100% true, however, and the problem below is a good example of a single equation in two variables which produce a single ordered pair solution.
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x3 + 12xy2 = 7x2y
x + y = 20
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x - y = 2
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