Hi Robert.

There are two variables and one equation, so that means there are many answers (you always need as many equations as variables if you want a single specific answer!)

So in fact, you have a line and any pair of numbers on the line will answer it. For example, if x is 0 and y is 8, that works. Also, if x is -3 and y is 3, it works. Also, if x is -24/5 and y is 0 it works. There are in fact an infinite number of "answers" because the equation you have represents a line and a specific pair of numbers is a point. Since there are an infinite number of points on a line, there are an infinite number of answers.

Note that I use the word "answer" to refer to a specific value.

A looser definition of "answer" would be that the answer to the question you asked "What is -5x +3y = 24" is just "a line."

Cheers,
Stephen La Rocque.