Big math question?

Question

Describe the three possible outcomes (solutions) to a system of two equations. For each possible solution, do the following:
•Explain the relationship between the graphs of the two lines
•Explain how the equations compare.


I gave some answers to this question which my teacher shot me down in the middle of class so I need a good answer so I can have a comback to my fall.

she is one of those teacher where if you mess up once your done for the rest of the class so I need a good comback answer which I ant think of.

Answer 1

I assume you mean two _linear_ equations in two variables, because otherwise there are more than three outcomes, and the graphs would not nessecarily be lines. With that restriction in mind:

#1: There is one solution: in this case the lines intersect at a point, and the equations are free to take any form except the two listed below.
#2: There are no solutions: in this case the lines are parallel, and the equations differ by a constant other than zero.
#3: There are infinitely many solutions: in this case the lines are the same, and the equations are the same up to rearrangement of the terms.

Note that if the equations are allowed to be nonlinear, you can have any finite number of solutions (by letting the equations be polynomials for instance) or an infinite number of solutions (say, with y=0 and y=sin x) without being the same curve. Also, you can have no solutions without having the two functions differ by a constant, see for instance y=x+1 and y=ln x.

Answer 2

2

Answer 3

A Unique Solution, No Solution and an infinite number of Solution.

Answer 4

Two lines can intersect in one point - ONE solution.

Two "lines" can be the same line - INFINITE solutions

Two lines can be parallel - NO solution

Answer 5

the appropriate thank you to bypass a math try is to check. paintings some equations which you think of could be such as those on the try, and become familiar with the thank you to unravel the equation.

Answer 6

Do your own homework