Exploring Graphs

Graphs of a pair of linear equations in two variables.

Case 1 Intersecting lines

Case 2 Parallel lines
Case 3 Coincident lines

Pair of linear equations in two variables

Points to remember:

• Graphical method of solving a pair of linear equations in two variables:

step 1 Consider the given set of equations and find ordered pairs (x,y) satisfying the given equations.

step 2. Plot the points obained on a graph paper and observe the type of lines.

Note the following:

1. If the graph of a pair of linear equations in two variables represent intersecting lines ,then there is a unique solution, and the given pair of equations is said to be consistent.

2. If the graph of a pair of linear equations in two variables represent coincident lines ,then there are infinitely many solutions , and the given pair of equations is said to be consistent.

3. If the graph of a pair of linear equations in two variables represent parallel lines ,then there is no solution, and the given pair of equations is said to be inconsistent.

• Conditions for consistency or inconsistency of a pair of linear equations in two variables.

Consider a pair of linear equtions in two variables
a1x + b1y = c1
a2x + b2y = c2
There are three cases:
Case 1 : For unique solution

Case 2: For No solution
Case 3:For infinitely many solutions

A way to express

Recently, one of my students sent to me these pictures expressing his thanks for making this class blog. I liked them so much, so I thought of uploading here.