Linear and QuadraticPro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear
Linear and Quadratic
Find all ordered pairs (x, y) such that:
3x - y = 10
x2 + 8x - y2 + 3y = 17
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Find the sum of x and y if x and y are positive numbers such that x2 + 3xy + y2 = 424 and xy = 100
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
Find all ordered pairs (x, y) such that
2x + xy + y = 18
x - y = 2
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).
Find all ordered pairs (x, y) such that the following two equations are true:
x2 - 4y2 = 108
x = 18 - 2y
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 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?
Solve for m and n.
(m + n)2 - 10(m + n) + 24 = 0
(m - n)2 + 6(m - n) + 8 = 0
Find all ordered pairs (x,y) which solve the following system of equations:
x3 + 12xy2 = 7x2y
x + y = 20
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?