1. Tardigrade
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  4. The value of λ For which the lines 3x+4y=5, 2x+3y=4 and λ x+4y=6 meet at a point, is:

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Q. The value of $ \lambda $ For which the lines $ 3x+4y=5, $ $ 2x+3y=4 $ and $ \lambda x+4y=6 $ meet at a point, is:

KEAMKEAM 2002

Solution:

The given lines are $ 3x+4y=5 $ ...(i) $ 2x+3y=4 $ ...(ii) and $ \lambda x+4y=6 $ ...(iii) on solving Eqs. (i) and (ii), we get $ x=-1 $ and $ y=2 $ All lines meet at a point, therefore the above point satisfies the Eq. (iii) $ \Rightarrow $ $ -\lambda +8=6 $ $ \Rightarrow $ $ \lambda =2 $