Pair Of Linear Equation In Two Variable
General form
Solutions
There are two methods to solve a pair of linear equation in two variables-
Graphical Representation
By Substitution
By Elimination
By Cross-multiplication
Unique solutions
Infinitely many solution
No solution
Intersecting lines
Coincident Lines
Parallel lines
- If line is parallel to y-axis then x will be constant
- If line is parallel to x-axis then y will be constant
Rules to write a liner equation in two variable
1) a1,b1and a2,b2 cannot be Zero
2) a1,a2,b1,b2,c1,c2,c2-Real numbers
Algebraic Methods
ax + by + c =0
Important Points ‼
- a₁/a₂ ≠ b₁/b₂ : In this case, the pair of linear equation is consistent.
- a₁/a₂ = b₁/b₂ ≠ c₁/c₂ : In this case, the pair of linear equation is inconsistent.
- a₁/a₂ = b₁/b₂ = c₁/c₂ : In this case, the pair of linear equation is dependent and consistent.