This document discusses three types of lines: intersecting lines, parallel lines, and coincident lines. Intersecting lines cross each other at a single point and have different slopes. Parallel lines have the same slope but do not intersect. Coincident lines have the same slope and the same points, so they overlap completely. It also provides examples of solving systems of linear equations graphically by finding the intersection points of the lines defined by the equations.

2. Intersecting Lines
Parallel Lines
Coincident Lines

3. Intersecting lines
Possible when
a1/a2 b1/b2
Parallel Lines
Possible when
A1/a2=b1/b2
=c1/c2
Coincident lines
Possible when
a1/a2=b1/b2
≠ C1/c2
≠

4. Equation1- x-2y=0
Equation2- 3x+4y=20
X 2 -4
Y 1 -2
X 0 4
Y 5 2
X X
Y
Y

5. Equation1- 2x+4y=12
Equation2- x+2y=4
X -2 2
Y 3 1
X 2 4
Y 2 1
X X
Y
Y

6. Equation1- 3x-y=2
Equation2- 9x-3y=6
X 2 1
Y 4 1
X 0 -1
Y -2 -5
X X
Y
Y