Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.
-The difference between the squares of two numbers is 80. Twice the square of the second number subtracted from the square of the first number is 16. Find the numbers.
A)12 and 8
B)12 and 8; -12 and 8; 12 and -8; -12 and -8
C)12 and 8; -12 and -8
D)12 and 8; -12 and 8; 12 and -8

Question

Quizplus · Accepted Answer

The system of nonlinear equations based on the given conditions is $x^2 - y^2 = 80$ and $x^2 - 2y^2 = 16$. Solving this system yields four pairs of solutions: $12$ and $8$, $-12$ and $8$, $12$ and $-8$, $-12$ and $-8$, because both equations are symmetric with respect to $x$ and $y$, allowing for both positive and negative solutions for each variable.

Let X Represent One Number and Let Y Represent the Other