Games
Problems
Go Pro!

One Equation, Two Variables

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

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

Presentation mode
Problem by Mr. Twitchell

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

Quadratic System

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

x2 - 4y2 = 108

x = 18 - 2y

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).

 

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

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

x2 + 8x - y2 + 3y = 17
 

Cubic and Linear

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

x3 + 12xy2 = 7x2y

x + y = 20

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)

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.

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?

Sum and Product System, Mary and Laura's Cookies, X and Y System

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

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