Question

A system of 2 linear equations is ___ dimensional. It is a graph of _____ lines. The solutions can be _____ solution if the graph intersects. _____ solution if the lines are parallel - meaning they have the same slope, or ___ solutions if they are the same line.

Answer 1

Considering High School level question, answer can be written as:

A system of 2 linear equations is [two] dimensional. It is a graph of [two] lines. The solutions can be [unique] solution if the graph intersects. [No] solution if the lines are parallel - meaning they have the same slope, or [Infinitely many] solutions if they are the same line.

Explanation:

when two lines are drawn on a two-dimensional plane then there are only three possible cases:

Case1: lines will intersect

In that case you will get a unique solution at the intersection point.

Case2: lines are parallel but don't touch each other

In that case there will be no point which lies on both lines so No solution.

Case3: lines are overlapping.

In that case all the points lies on both lines so infinitely many solutions.