Question

How many solutions does the following system have?
y = -2/3 x + 3 and 2x + 3y = 9?

Answer 1

one solution

no solution

infinitely many solutions

cannot be determined

Answer 2

well, it is the same linear equation

Answer 3

so its one solution?

Answer 4

well, I don't really know what you mean by how many solutions does it have

Answer 5

idk either thats what the questions says im not adding any words

Answer 6

the value of y depends on the value x and the value of x can technically be any value

Answer 7

along the Cartesian plane

Answer 8

ight thanks for trying

Answer 9

Since both equations are transformed versions of each other, we only really have one equation in a system with two variables. In other words, you can pick any y value and get a valid answer for x because there's no second equation to consider. Thus the system have infinite solutions.

Answer 10

there we go ty!

Answer 11

well, usually when you are presented with a system of linear equations your goal is to determine where the two will intersect.

Answer 12

I have not seen a question in this format before lol, but seeing as the two equations represent the same line, I guess that it would be true to state that there are no domain and range restrictions and that x and y can represent any value.

Answer 13

Well, yes, that is usually the general idea of what you're supposed to be doing for this. When you have more than three dimentions, however, you can't really visualize it in that regard. Whenever you have more variables than pivot equations to work with, that's usually when you have an infinite amount of solutions in a system.