Games
Problems
Go Pro!

Product of X and Y

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

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).

 

Presentation mode
Problem by allie

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

Similar Problems

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)

Quadratic System

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

x2 - 4y2 = 108

x = 18 - 2y

Cubic and Linear

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

x3 + 12xy2 = 7x2y

x + y = 20

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?

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 x2 + y2 - 2x + 4y = -5

Linear and Quadratic

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

3x - y = 10

x2 + 8x - y2 + 3y = 17
 

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

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?

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

System with a Product

Find all ordered pairs (x, y) such that

2x + xy + y = 18

x - y = 2

System with Radical, Mary and Laura's Cookies, Quadratic System

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy