One Equation, Two VariablesPro 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
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Find all ordered pairs (x, y) such that the following two equations are true:
x2 - 4y2 = 108
x = 18 - 2y
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
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) such that:
3x - y = 10
x2 + 8x - y2 + 3y = 17
Find all ordered pairs (x,y) which solve the following system of equations:
x3 + 12xy2 = 7x2y
x + y = 20
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)
Find all ordered pairs (x, y) such that
2x + xy + y = 18
x - y = 2
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.
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?