For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions? ?->(Show Answer!)

1. For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?

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By: anil on 05 May 2019 02.06 am

For the two equations to have infinite number of solutions, the two lines must overlap one another. Lines having equation $$a_1x+b_1y+c_1=0$$ and $$a_2x+b_2y+c_2=0$$ are said to be collinear if $$frac{a_1}{a_2}$$ $$=frac{b_1}{b_2}$$ $$=frac{c_1}{c_2}$$ Thus, for the equations : 6x + 12y + 9 = 0 and 2x + gy + 3 = 0 => $$frac{6}{2}=frac{12}{g}=frac{9}{3}$$ => $$frac{12}{g}=3$$ => $$g=frac{12}{3}=4$$ => Ans - (B)

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