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

intersecting-lines-1024x478

coincident_lines

examples-of-parallel-lines (1)

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.