Pair of Linear Equations in Two Variables

1. Algebraic Methods

1.1. By Substitution

1.2. By Elimination

1.3. By Cross-Multiplication

2. Graphical Representation

2.1. Unique Solution

2.1.1. Intersecting Lines

2.2. Infinitely Many Solutions

2.2.1. Coincident Lines

2.3. No Solution

2.3.1. Parallel Lines

3. Rules

3.1. a1, a2, b1, b2, c1, c2-Real numbers

3.2. a1, b1 and a2, b2 cannot be Zero simultaneously

4. General Form

4.1. a1x+b1y+c1=0 and a2x+b2y+c2=0

5. Solutions

5.1. Algebraically

5.2. Graphically

6. Equations for:-

6.1. x-axis: y=0

6.2. y-axis: x=0

6.3. Line parallel to y-axis: x=constant

6.4. Line parallel to x-axis: y=constant