Question

What is the nature of the graphs of the system of linear equations with exactly one solution?
A.Parallel lines
B.Perpendicular lines
C.Coincident lines
D.Intersecting lines

Answer 1

Hint: In the given question, we have been asked what is the system of linear equations called which have just one solution. For answering that, we must know what does it mean to have just one solution.

Complete step-by-step answer:
A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct.
In the given question, we have been asked what do we call a system of linear equations which have just one solution, i.e., when these equations are represented as lines, they intersect at just one place.
Now, we know that the lines that intersect at just one place are called intersecting lines and the system of equations is said to be consistent.
So, the correct answer is “Option D”.

Note: When both equations have the same slope, but not the same y-intercept, they'll be parallel to each other and no intersections means no solutions. When both equations have different slopes than regardless of the y-intercept they'll intersect for certain, therefore it has exactly one solution.