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