Question

Is it possible for a system of linear equations to have exactly two solution?

Answer 1

it is very possible

y = x² and y = cos(x)

Answer 2

but cox is not a linear equation?

Answer 3

and x^2 as well

Answer 4

I misread I apologies

Answer 5

all good :)

Answer 6

No it cannot. Because neither x or y (or what your variables are) aren't raised to a second power, they don't have multiple answers. x has one answer, y has one answer. It can have infinite solutions, if any number you put for x will be equal to y. (x = y)

Here's an example of a one solution problem:

2x - y = -1

-x + y = 3

you add them to get x = 2 and put x in to get y = 5

Here's one of infinite solutions:

x - 1/2y = -6

-4x + 2y = 24

Add them to get 0 = 0 which means anything will work! Try putting something like 4 and y will come out 4

Here's one with no solutions:

x - y = 23

-x + y = -18

Add and you get 0 = 5 which means nothing will work (try it)

Think of a graph. We have an x line and a y line. If they touch each other and aren't parallel, where they touch each other is the solution. If they are right on top of each other (parallel) infinite solutions!! It goes on and on. The other is they are parallel and don't touch at all. No solutions.