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• Two linear equations in the same two variables are said to form a pair of linear equations in two variables.
• The most general form of a pair of linear equations is
a1x + b1 y + c1 = 0
a2x + b2 y + c2 = 0,
where a1, a2, b1,b2, c1, c2 are real numbers, such that a12 b12 0,a22 b22 0 .
• A pair of linear equations is consistent if it has a solution – either a unique or infinitely many. In case of infinitely many solutions, the pair of linear equations is also said to be dependent. Thus, in this case, the pair of linear equations is dependent and consistent.
• A pair of linear equations is inconsistent, if it has no solution.
• Let a pair of linear equations in two variables be a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0.
(I) If a1/a2 b1/ b2
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NCERT Book for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables
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