A system of three equations in two unknowns corresponds to t

A system of three equations in two unknowns corresponds to three lines in the plane. Describe several ways that these lines might be positioned if the system has no solutions. (Select all that apply.)

The lines are all parallel.

Two of the lines are the same, and the third line intersects it in a single point.

The three lines intersect in a single point.

The three lines intersect in three different points (forming a triangle).

Two of the lines are parallel.

Solution

It implies that the three lines do not intercept at one common point.

possibility (1) :-

All the lines could either be parallel where none of them would intersect with each other or we could have two of them intersecting but the three lines intersecting each other at three different points.

Possibility (2)

We could also have two lines parallel to each other and the third line intersecting with these.

Possibility (3)

If The lines are all parallel

Possibility (4)

The three lines intersect in three different points (forming a triangle)

in this condition there will not be any single point