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Sum of X and Y

Pro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear
 

Sum of X and Y

Find the sum of x and y if x and y are positive numbers such that x2 + 3xy + y2 = 424 and xy = 100

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To Sum It Up

I have picked three positive integers for the lottery, as follows: The sum of my numbers is 54. The sum of my numbers, plus the sum of two of my numbers, is 84. The sum of the squares of my numbers is 1034. What are the three integers?

Linear and Quadratic

Find all ordered pairs (x, y) such that:

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One Equation, Two Variables

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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Product of X and Y

For the ordered pair (x,y) the product of x and y is 108. If x + 2y = 30, find all possible ordered pairs (x,y).

 

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Find the sum of x and y, if the following are true:

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Find all ordered pairs (x,y) which solve the following system of equations:

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