This lesson is on solving systems of linear equations using graphs. In this lesson, you will find solutions by looking for the correct graph.

A SYSTEM OF TWO LINEAR EQUATIONS
3 Possibilities

Intersecting lines – One solution
Parallel lines – No solution
Coinciding lines – Infinite solutions

As shown above, there are only three situations possible for a system of two linear equations. If the lines are intersecting lines, the solution is the coordinate point where the lines meet. When the lines are parallel lines, they do not cross and there is no solution. When the lines are the same line, they are called coinciding lines and have infinite solutions because any point on one line is also on the other line. The following 3 graphs show these types of solutions.

Three graphs are shown. The graph labeled intersecting lines shows 2 lines that intersect at one specific point; the graph labeled parallel lines shows 2 parallel lines; the graph labeled coinciding lines shows 2 lines with the second line lying on top of the first line