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# Sum and Product System

Pro 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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Problem by allie

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## Similar Problems

The sum of two numbers is seven times the difference between three times the second number and twice the first number. If the second number is subtracted from the first, the result is the square root of the first. Find all possible values for the first number.

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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.

Solve for the ordered pair (x,y) such that x2 + y2 - 2x + 4y = -5

Solve for m and n.

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

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(x + 1)(x + 3) = (y - 5)(y - 7)

### 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).

### Cubic and Linear

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

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

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### 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

### System with a Product

Find all ordered pairs (x, y) such that

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X and Y System, Quadratic System, To Sum It Up

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