Question

Recall that variables represent changing values. In this unit, you will work with equations that contain two different variables. What types of situations might be modeled with equations containing two or more variables? If the value of one variable changes, must the value of the other variable change for the equation to remain true? How would the number of solutions for an equation with two variables differ from the number of solutions for an equation with only one? Explain.

Answer 1

For example, afunction that gives a temperature as you move in the right/left forward/backward or down/up directions.

Answer 2

in general (in 3D) these are x, y, and z directions.

Answer 3

This would qualify as a possible general case, ok?

Answer 4

(What I say from now, is in general, and not particularly related to this case, exactly....)

Then, you know that equations with 1 variable have 1 solution.
For example, x-5=4 can have only one solution (and that is x=9).

However, if you have x+y=5, then regardless of the value of x
you choose, you still have some solution for y that makes a
statement true. So if you were to choose x=2, and from that
you now have 2+y=5, you still have a true statement by, y=3.

And if you have a function of 3 variables, you can change two
of the variables, and your equation/statement still holds.

Answer 5

I am not trying to give you the answer, really, rather the information.