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If a1x + b1y + c1 = 0 a2x + b2y + c2 = 0 is a pair of linear equations in two variables x and y.How do you know if an equation is consistent or inconsistent? |
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Answer» If a1x + b1 y + c1 = 0 a2x + b2y + c2 = 0 is a pair of linear equations in two variables x and y such that : (i) \(\frac{a_1}{a_2}\) \(\ne\) \(\frac{b_1}{b_2}\),then the pair of linear equations is consistent with a unique solution, i.e., they intersect at a point. (ii) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) \(\ne\) \(\frac{c_1}{c_2}\),then the pair of linear equations inconsistent with no solution, i.e., they represent a pair of parallel lines. (iii) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\), then the pair of linear equations are consistent with infinitely many solutions, i.e., they represent coincident lines. |
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