Which of the following pairs of linear equations are consistent / inconsistent if consistent obtain the solution graphocally
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Graphical Method of solving pair of linear equations in two variables
The general form for a pair of linear equations in two variables x and y is
a1x + b1y + c1 = 0 ,
a2x + b2y + c2 = 0 ,
Where a1, a2, b1, b2, c1, c2 are all real numbers ,a1²+ b1² ≠ 0 & a2² + b2² ≠ 0.
Condition 1: Intersecting Lines
If a 1 / a 2 ≠ b 1 / b 2 , then the pair of linear equations has a unique solution.
Condition 2: Coincident Lines
If a 1 / a 2 = b 1 / b 2 = c 1 / c 2 ,then the pair of linear equations has infinite solutions.
A pair of linear equations, which has a unique or infinite solutions are said to be a consistent pair of linear equations.
A pair of linear equations, which has infinite many distinct common solutions are said to be a consistent pair or dependent pair of linear equations.
Condition 3: Parallel Lines
If a 1/ a 2 = b 1/ b 2 ≠ c 1 / c 2 , then a pair of linear equations has no solution.
A pair of linear equations which has no solution is said to be an inconsistent pair of linear equations.