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If 2a = b, the pair of equations ax + by = 2a2 – 3b2 , x + 2y = 2a – 6b possess : (a) no solution (b) only one solution (c) only two solutions (d) an infinite number of solutions |
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Answer» (d) an infinite number of solutions Here a1 = a, b1 = b, c1 = – (2a2 – 3b2 ) = 3b2 – 2a2 a2 = 1, b2 = 2, c2 = – (2a – 6b) = 6b – 2a \(\frac{a_1}{a_2}=\frac{a}{1}\), \(\frac{b_1}{b_2}=\frac{b}{2}\),\(\frac{c_1}{c_2}\)= \(\frac{3b^2-2a^2}{6b-2a}\) 2a = b \(\Rightarrow\) a = \(\frac{b}{2}\) \(\therefore\) \(\frac{a_1}{a_2}=\frac{b}{2}\), \(\frac{b_1}{b_2}=\frac{b}{2}\) and \(\frac{c_1}{c_2}\)= \(\frac{3b^2-2\times\frac{b^2}{4}}{6b-2\times\frac{b}{2}}\)= \(\frac{3b^2-\frac{b^2}{2}}{6b-b}\) = \(\frac{\frac{5b^2}{2}}{5b}\)=\(\frac{b}{2}\) \(\therefore\) \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) |
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