Linear and Quadratic
Pro Problems > Math > Algebra > Equations > Systems of Equations > Non-LinearLinear and Quadratic
Find all ordered pairs (x, y) such that:
3x - y = 10
x2 + 8x - y2 + 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
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.
Quadratic System
Solve for m and n.
(m + n)2 - 10(m + n) + 24 = 0
(m - n)2 + 6(m - n) + 8 = 0
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?
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
Find all ordered pairs (x, y) such that the following two equations are true:
x2 - 4y2 = 108
x = 18 - 2y
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)
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?
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
Blogs on This Site
Like us on Facebook to get updates about new resources