Pair of Linear Equations in Two Variables

1. General Form

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

2. Solutions

2.1. Algebraically

2.2. Graphically

3. Algebraic Methods

3.1. By Substitution

3.2. By Elimination

3.3. By Cross-Multiplication

4. Graphical Representation

4.1. Unique Solution

4.1.1. Intersecting Lines

4.2. Infinitely Many Solutions

4.2.1. Coincident Lines

4.3. No Solution

4.3.1. Parallel Lines

5. Equations for:-

5.1. x-axis: y=0

5.2. y-axis: x=0

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

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

6. Rules

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

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