# Linear and Quadratic

Pro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear## Linear and Quadratic

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

3x - y = 10

x^{2} + 8x - y^{2} + 3y = 17

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### Quadratic System

Solve for m and n.

(m + n)^{2} - 10(m + n) + 24 = 0

(m - n)^{2} + 6(m - n) + 8 = 0

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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?

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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.

Solve for the ordered pair (x,y) such that x^{2} + y^{2} - 2x + 4y = -5

### System with a Product

Find all ordered pairs (x, y) such that

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