Sum of X and YPro Problems > Math > Algebra > Equations > Systems of Equations > Non-Linear
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
SolutionIn 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.
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 the following two equations are true:
x2 - 4y2 = 108
x = 18 - 2y
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 all ordered pairs (x,y) which solve the following non-linear system of equations.
x(x - 2y) - 4 = 2y(x - 2y)
x + 2y = 10
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
2x + xy + y = 18
x - y = 2
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
Find all ordered pairs (x, y) such that:
3x - y = 10
x2 + 8x - y2 + 3y = 17
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).
Educators can get a free membership simply by sharing an original lesson plan on our Articles for Educators page!