# X and Y Quadratics

Pro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear## X and Y Quadratics

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

(x + 2)(x - 1) = (y - 12)(y + 3)

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

## 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

### Mary and Laura's Cookies

Mary and Laura Ingalls each receive a cookie. Because they are thoughtful children, they want to share with their little sister Carrie. Because their math skills aren't very advanced, they each eat half of a cookie, but then realize that leaves a full cookie for Carrie.

How much should each girl eat in order to share equally among the three sisters?

### 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?

### Cubic and Linear

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

x^{3} + 12xy^{2} = 7x^{2}y

x + y = 20

### Sum of X and Y

Find the sum of x and y if x and y are positive numbers such that x^{2} + 3xy + y^{2} = 424 and xy = 100

### System with a Product

Find all ordered pairs (x, y) such that

2x + xy + y = 18

x - y = 2

### System with Radical

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.

### 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).

### 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?

### Quadratic System

Solve for m and n.

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

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

### Linear and Quadratic

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

3x - y = 10

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