Assuming that x and y are the same.

Hi Lstadt

That's a good question.

Whenever the question explicitly mentions two variables, say x and y, you are supposed to assume that x and y are numbers with different values. Although, on solving for the answer, you might realize that they both have same values i.e. a single number can be the value for both x and y such that the given system of equations/inequalities/conditions are satisfied.

For example, consider the two equations
x + y = 9 and
x - y = 1
We can solve these two equations to get the unique answer as x = 5 and y = 4.

However, consider the following equation
(x^2)/(y^2) = 1
The above equation means that both x and y have the same absolute value i.e. |x| = |y|
Consider the values x = 2 and y = -2 --> These values satisfy the equation
So does the values x = 3 and y = 3

So, we can say that, for the purpose of solving the question, we have to assume that the values of x and y are different. However, in cases such as inequalities, wherein you need to consider varied values, it might so happen that the same value for x and y will satisfy the given equation/inequality.

Hope this helps

Cheers!