Pair of Linear Equations in Two Variables — Important Questions

Algebraic method

Algebraic methods like substitution and elimination are more precise for solving equations with complex coordinates.

Substitution method

In the substitution method, one variable is expressed in terms of another and then substituted into the second equation.

Has a solution

A consistent pair of linear equations means the system has at least one solution, either unique or infinite.

a1/a2 = b1/b2 ≠ c1/c2

For a pair of linear equations, parallel lines satisfy the condition a1/a2 = b1/b2 ≠ c1/c2. This means the coefficients of x and y are proportional, but the constant terms are not in the same ratio. Such lines do not meet, so the pair has no solution.