Go Pro!

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)

Presentation mode
Problem by Mr. H


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.
Assign this problem
Click here to assign this problem to your students.

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

Cubic and Linear

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

x3 + 12xy2 = 7x2y

x + y = 20

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

Find all ordered pairs (x, y) such that the following two equations are true:

x2 - 4y2 = 108

x = 18 - 2y

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?

System with a Product

Find all ordered pairs (x, y) such that

2x + xy + y = 18

x - y = 2

Linear and Quadratic

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

3x - y = 10

x2 + 8x - y2 + 3y = 17

X and Y System

Find all ordered pairs (x,y) which solve the following non-linear system of equations.

x(x - 2y) - 4 = 2y(x - 2y)

x + 2y = 10

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).


Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!
Like us on Facebook to get updates about new resources
Pro Membership