Question

1. How can graphing methods be used to solve a system of linear equations, and how can you determine the equations of the two lines by analyzing the graph?

Answer 1

Solving a linear system by Graphical Methods :

Suppose graph of two lines are drawn on a same set of axes.

Then we have the following cases.

Case I : If the two graphs intersect at any point, then there is a unique solution and the solution becomes the intersection point of the graphs.

Case II : If the graphs are same, then there are infinitely many solutions.

Case III : If both the graphs are parallel then they will never intersect which means the system will have no solution.