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9. straight line — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS9. straight line1 Mark
MCQ
The value of $\lambda $ for which the lines $3x + 4y = 5,$ $5x + 4y = 4$ and $\lambda x + 4y = 6$ meet at a point is
  • A
    $2$
  • ✓
    $1$
  • C
    $4$
  • D
    $3$
✓

Answer

Correct option: B.
$1$
b
(b) Given lines are $3x + 4y = 5,$ $5x + 4y = 4,$ $\lambda x + 4y = 6$. These lines meet at a point if the point of intersection of first two lines lies on the third line.

From $3x + 4y = 5$ and $5x + 4y = 4$

We get $x = \frac{{ - 1}}{2},$ $y = \frac{{13}}{8}$

This lies on $\lambda x + 4y = 6,$ if $\lambda \,\left( { - \frac{1}{2}} \right) + 4\left( {\frac{{13}}{8}} \right) = 6$

==> $\lambda = 1$.

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