A system of three equations in two unknowns corresponds to three lines in the plane. Describe how these lines might be positioned if the system has no solutions ?
A)The three lines could form a triangle.
B) There could be two parallel lines, with a third crossing them.
C) The three lines intersect at a single point.
D) There could be two parallel lines.
E) The three lines intersect at a single point, but two of the lines are the same and the third one crosses them.

Question

A system of three equations in two unknowns corresponds to three lines in the plane. Describe how these lines might be positioned if the system has no solutions  ?
A)The three lines could form a triangle.
B) There could be two parallel lines, with a third crossing them.
C) The three lines intersect at a single point.
D) There could be two parallel lines.
E) The three lines intersect at a single point, but two of the lines are the same and the third one crosses them.

Quizplus · Accepted Answer

If a system of three equations in two unknowns has no solutions, it means that there is no single point that satisfies all three equations simultaneously. This can happen if the lines form a triangle (A), indicating that each pair of lines intersects at a different point, or if there are two parallel lines with a third crossing them (B), or simply two parallel lines (D), where at least one pair of lines does not intersect at all, preventing a common solution.

A System of Three Equations in Two Unknowns Corresponds to Three