Question

The graph of a system of linear equations results in 2 intersecting lines.
Which of the following is true about this graph?

A.The system has 1 solution

B. The system has no solutions.

C. The system has infinite solutions

D. Not enough information

Answer 1

A.The system has 1 solution

Answer 2

The system has infinite solutions

Answer 3

No, the lines only interect once. THey are no the same line.

Answer 4

where is it mentioned they intersect once?

Answer 5

they can be coincident

Answer 6

right??
or am i taking it in a wrong way??

Answer 7

If they are coincident, then they are the same line (in effect).

Answer 8

yes but they can also intersect at all places..
thats how we get infinite solutions no?

Answer 9

same set of points

Answer 10

estudier?
am i wrong?

Answer 11

Intersection 8without any qualification) is usually taken to mean 1 solution....

Answer 12

okay.

Answer 13

As to whether u are wrong, I think it's really a philosophical question....:-)

Answer 14

lol!
i was right then..

Answer 15

Systems of two equations in two real-value unknowns usually appear as one of five different types, having a relationship to the number of solutions:

Systems that represent intersecting sets of points such as lines and curves, and that are not of one of the types below. This can be considered the normal type, the others being exceptional in some respect. These systems usually have a finite number of solutions, each formed by the coordinates of one point of intersection.
Systems that simplify down to false (for example, equations such as 1 = 0). Such systems have no points of intersection and no solutions. This type is found, for example, when the equations represent parallel lines.
Systems in which both equations simplify down to an identity (for example, x = 2x − x and 0y = 0). Any assignment of values to the unknown variables satisfies the equations. Thus, there are an infinite number of solutions: all points of the plane.
Systems in which the two equations represent the same set of points: they are mathematically equivalent (one equation can typically be transformed into the other through algebraic manipulation). Such systems represent completely overlapping lines, or curves, etc. One of the two equations is redundant and can be discarded. Each point of the set of points corresponds to a solution. Usually, this means there are an infinite number of solutions.
Systems in which one (and only one) of the two equations simplifies down to an identity. It is therefore redundant, and can be discarded, as per the previous type. Each point of the set of points represented by the other equation is a solution of which there are then usually an infinite number.